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On the Miura map between the dispersionless KP and dispersionless modified KP hierarchiesDec 29 1999We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and Takebe, the ... More

Commuting difference operators with elliptic coefficients from Baxter's vacuum vestorsDec 28 1999Jan 12 2000For quantum integrable models with elliptic R-matrix, we construct the Baxter Q-operator in infinite-dimensional representations of the algebra of observables.

Monodromy transform approach to solution of the Ernst equations in General RelativityDec 27 1999The approach, referred to as "monodromy transform", provides some general base for solution of all known integrable space - time symmetry reductions of Einstein equations for the case of pure vacuum gravitational fields, in the presence of gravitationally ... More

Vector NLS hierarchy solitons revisited: dressing transformation and tau function approachDec 27 1999We discuss some algebraic aspects of the integrable vector non-linear Schr\"{o}dinger hierarchies (GNLS$_{r}$). These are hierarchies of zero-curvature equations constructed from affine Kac-Moody algebras $\hat{sl}_{r+1}$. Using the dressing transformation ... More

Vertex operator solutions to the discrete KP-hierarchyDec 23 1999Vertex operators, which are disguised Darboux maps, transform solutions of the KP equation into new ones. In this paper, we show that the bi-infinite sequence obtained by Darboux transforming an arbitrary KP solution recursively forward and backwards, ... More

Singular solution of the Liouville equation under perturbationDec 22 1999Small perturbation of the Liouville equation under singular initial data is considered. An asymptotics of the singular solution is constructed by the method which is similar to Bogolubov -- Krylov one. The main object is an asymptotics of the singular ... More

Calogero-Moser systems and Hitchin systemsDec 20 1999We exhibit the elliptic Calogero-Moser system as a Hitchin system of G-principal Higgs pairs. The group G, though naturally associated to any root system, is not semi-simple. We then interpret the Lax pairs with spectral parameter of [dP1] and [BSC1] ... More

Whitham-Toda Hierarchy in the Laplacian Growth ProblemDec 18 1999The Laplacian growth problem in the limit of zero surface tension is proved to be equivalent to finding a particular solution to the dispersionless Toda lattice hierarchy. The hierarchical times are harmonic moments of the growing domain. The Laplacian ... More

Thermodynamic Bethe ansatz equation from fusion hierarchy of osp(1|2) integrable spin chainDec 17 1999Jul 03 2000The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp(1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of the QTM and derive ... More

Liouville equation under perturbationDec 16 1999Small perturbation of the Liouville equation under smooth initial data is considered. Asymptotic solution which is available for a long time interval is constructed by the two scale method.

Real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspacesDec 15 1999Oct 01 2000Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is demonstrated that they possess a global twisted N=2 supersymmetry. We discuss a new superfield ... More

Exact Dynamics of the SU(K) Haldane-Shastry ModelDec 15 1999The dynamical structure factor $S(q,\omega)$ of the SU(K) (K=2,3,4) Haldane-Shastry model is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of free quasi-particles which are generalization of spinons ... More

Duality in Integrable Systems and Generating Functions for New HamiltoniansDec 14 1999Dec 24 1999Duality in the integrable systems arising in the context of Seiberg-Witten theory shows that their tau-functions indeed can be seen as generating functions for the mutually Poisson-commuting hamiltonians of the {\em dual} systems. We demonstrate that ... More

Quantum Lax Pair From Yang-Baxter EquationsDec 14 1999We show explicitly how to construct the quantum Lax pair for systems with open boundary conditions. We demonstrate the method by applying it to the Heisenberg XXZ model with general integrable boundary terms.

Exact dynamical structure factor of the degenerate Haldane-Shastry modelDec 14 1999The dynamical structure factor $S(q,\omega)$ of the K-component (K = 2,3,4) spin chain with the 1/r^2 exchange is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of a free quasi-particle picture ... More

Riemann-Hilbert problem and the discrete Bessel kernelDec 12 1999Mar 09 2000We use discrete analogs of Riemann-Hilbert problem's methods to derive the discrete Bessel kernel which describes the poissonized Plancherel measures for symmetric groups. To do this we define discrete analogs of a Riemann-Hilbert problem and of an integrable ... More

Integrable structures in classical off-shell 10D supersymmetric Yang-Mills theoryDec 10 1999Apr 14 2000The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness conditions were proposed, ... More

Frobenius submanifoldsDec 10 1999The notion of a Frobenius submanifold - a submanifold of a Frobenius manifold which is itself a Frobenius manifold with respect to structures induced from the original manifold - is studied. Two dimensional submanifolds are particularly simple. More generally, ... More

Vortices and invariants surfaces generated by symmetries for the 3D Navier-Stokes equationsDec 10 1999We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier-Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of vortices and throws ... More

The Pfaff lattice, Matrix integrals and a map from Toda to PfaffDec 06 1999We study the Pfaff lattice, introduced by us in the context of a Lie algebra splitting of gl(infinity) into sp(infinity) and lower-triangular matrices. We establish a set of bilinear identities, which we show to be equivalent to the Pfaff Lattice. In ... More

Dynamical Symmetry Approach to Periodic HamiltoniansDec 06 1999We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy bands and gaps ... More

Group Theoretical Properties and Band Structure of the Lame HamiltonianDec 06 1999We study the group theoretical properties of the Lame equation and its relation to su(1,1) and su(2). We compute the band structure, dispersion relation and transfer matrix and discuss the dynamical symmetry limits.

Generalized KP hierarchy: Möbius Symmetry, Symmetry Constraints and Calogero-Moser SystemDec 06 1999Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that M\"obius symmetry transformation for the singular manifold equation leads to continuous or discrete non-isospectral ... More

Integrable Couplings of Soliton Equations by Perturbations I. A General Theory and Application to the KdV HierarchyDec 03 1999A theory for constructing integrable couplings of soliton equations is developed by using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small perturbation parameter. Multi-scale perturbations can ... More

Toda lattice and toric varieties for real split semisimple Lie algebrasDec 02 1999Apr 06 2001The paper concerns the topology of an isospectral real smooth manifold for certain Jacobi element associated with real split semisimple Lie algebra. The manifold is identified as a compact, connected completion of the disconnected Cartan subgroup of the ... More

N=4 Sugawara construction on affine sl(2|1), sl(3) and mKdV-type superhierarchiesNov 30 1999Dec 07 1999The local Sugawara constructions of the "small" N=4 SCA in terms of supercurrents of N=2 extensions of the affinization of the sl(2|1) and sl(3) algebras are investigated. The associated super mKdV type hierarchies induced by N=4 SKdV ones are defined. ... More

Nonstandard coproducts and the Izergin-Korepin open spin chainNov 29 1999Dec 13 1999Corresponding to the Izergin-Korepin (A_2^(2)) R matrix, there are three diagonal solutions (``K matrices'') of the boundary Yang-Baxter equation. Using these R and K matrices, one can construct transfer matrices for open integrable quantum spin chains. ... More

Quantum Lax scheme for Ruijsenaars modelsNov 26 1999We develop a quantum Lax scheme for IRF models and difference versions of Calogero-Moser-Sutherland models introduced by Ruijsenaars. The construction is in the spirit of the Adler-Kostant-Symes method generalized to the case of face Hopf algebras and ... More

Construction of variable mass sine-Gordon and other novel inhomogeneous quantum integrable modelsNov 26 1999The inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact integrability inspite of their explicit inhomogeneity. Such ... More

Equations and Integrals of Motion in Discrete Integrable $A_{k-1}$ Algebra ModelsNov 19 1999We study integrals of motion for Hirota bilinear difference equation that is satisfied by the eigenvalues of the transfer-matrix. The combinations of the eigenvalues of the transfer-matrix are found, which are integrals of motion for integrable discrete ... More

Multidimensional analogs of geometric s<-->t dualityNov 18 1999Nov 24 1999The usual propetry of s<-->t duality for scattering amplitudes, e.g. for Veneziano amplitude, is deeply connected with the 2-dimensional geometry. In particular, a simple geometric construction of such amplitudes was proposed in a joint work by this author ... More

Separation of variables for soliton equations via their binary constrained flowsNov 17 1999Binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices have 2N degrees of freedom, which is twice as many as degrees of freedom in the case of mono-constrained flows. For their separation of variables only N pairs of canonical ... More

Bicomplexes and finite Toda latticesNov 16 1999We associate bicomplexes with the finite Toda lattice and with a finite Toda field theory in such a way that conserved currents and charges are obtained by a simple iterative construction.

Non-local Symmetries of Nonlinear Field Equations: an Algebraic ApproachNov 16 1999An algebraic method is devised to look for non-local symmetries of the pseudopotential type of nonlinear field equations. The method is based on the use of an infinite-dimensional subalgebra of the prolongation algebra $L$ associated with the equations ... More

Einstein metrics, hypercomplex structures and the Toda field equationNov 16 1999We obtain explicitly all solutions of the SU(infinity) Toda field equation with the property that the associated Einstein-Weyl space admits a 2-sphere of divergence-free shear-free geodesic congruences. The solutions depend on an arbitrary holomorphic ... More

Monodromy Transform Approach to Solution of Some Field Equations in General Relativity and String TheoryNov 11 1999Dec 09 2000A monodromy transform approach, presented in this communication, provides a general base for solution of space-time symmetry reductions of Einstein equations in all known integrable cases, which include vacuum, electrovacuum, massless Weyl spinor field ... More

Geodesic equivalence and integrabilityNov 10 1999We suggest a construction that, given a trajectorial diffeomorphism between two Hamiltonian systems, produces integrals of them. As the main example we treat geodesic equivalence of metrics. We show that the existence of a non-trivially geodesically equivalent ... More

Dynamical and Topological methods in Theory of Geodesically Equivalent MetricsNov 09 1999This paper is a review on recently found connection between geodesically equivalent metrics and integrable geodesic flows. Suppose two different metrics on one manifold have the same geodesics. We show that then the geodesic flows of these metrics admit ... More

Thermodynamic Bethe ansatz equation for osp(1|2) integrable spin chainNov 09 1999The thermodynamic Bethe ansatz is applied to a quantum integrable spin chain associated with the Lie superalgebra osp(1|2). Using the string hypothesis, we derive a set of infinite number of non-linear integral equations (thermodynamic Bethe ansatz equation), ... More

On the quantum inverse scattering problemNov 04 1999A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for ... More

A note on real forms of the complex N=4 supersymmetric Toda chain hierarchy in real N=2 and N=4 superspacesNov 04 1999Nov 20 1999Three inequivalent real forms of the complex N=4 supersymmetric Toda chain hierarchy (Nucl. Phys. B558 (1999) 545, solv-int/9907004) in the real N=2 superspace with one even and two odd real coordinates are presented. It is demonstrated that the first ... More

Integrable deformations of oscillator chains from quantum algebrasNov 03 1999A family of completely integrable nonlinear deformations of systems of N harmonic oscillators are constructed from the non-standard quantum deformation of the sl(2,R) algebra. Explicit expressions for all the associated integrals of motion are given, ... More

Resonant BifurcationsNov 03 1999We consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we discuss the existence -- under suitable hypotheses -- of a general ... More

The structure of quotients of the Onsager algebra by closed idealsNov 03 1999Jun 28 2000We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of ... More

Backlund Transformations in 10D susy Yang-Mills TheoriesNov 02 1999This is a continuation of hep-th/9811108, hep-th/9903218, hep-th/9910235, on exact integration technics for modified dynamical equations in ten dimensional supersymmetric gauge theory. A B\"acklund transformation is derived for the Yang type (super) equations ... More

Introduction to the functions on compact Riemann surfaces and theta-functionsNov 02 1999We collect some classical results related to analysis on the Riemann surfaces. The notes may serve as an introduction to the field: we suppose that the reader is familiar only with the basic facts from topology and complex analysis. the treatment is organized ... More

Integral representation for the eigenfunctions of quantum periodic Toda chainNov 01 1999Nov 02 1999Integral representation for the eigenfunctions of quantum periodic Toda chain is constructed for N-particle case. The multiple integral is calculated using the Cauchy residue formula. This gives the representation which reproduces the particular results ... More

Operator-valued Riemann-Hilbert problem for correlation functions of the XXZ spin chainOct 30 1999Dec 16 1999The generating functional of correlation functions for the XXZ spin chain is considered in the thermodynamic limit. We derive a system of integro-difference equations that prescribe this functional. On the basis of this system we establish the operator-valued ... More

Solution of the quantum inverse problemOct 30 1999We derive a formula that expresses the local spin and field operators of fundamental graded models in terms of the elements of the monodromy matrix. This formula is a quantum analogue of the classical inverse scattering transform. It applies to fundamental ... More

Canonical transformations of the time for the Toda lattice and the Holt systemOct 29 1999For the Toda lattice and the Holt system we consider properties of canonical transformations of the extended phase space, which preserve integrability. The separated variables are invariant under change of the time. On the other hand, mapping of the time ... More

The averaging of non-local Hamiltonian structures in Whitham's methodOct 28 1999Feb 28 2004We consider the $m$-phase Whitham's averaging method and propose the procedure of "averaging" of non-local Hamiltonian structures. The procedure is based on the existence of a sufficient number of local commuting integrals of the system and gives the ... More

Solution Generating in Ten Dimensional Supersymmetric Classical Yang--Mills TheoriesOct 28 1999In a recent paper (hep-th/9811108), Saveliev and the author showed that there exits an on-shell light cone gauge where the non-linear part of the field equations reduces to a (super) version of Yang's equations which may be solved by methods inspired ... More

Form factors of the SU(2) invariant massive Thirring model with boundary reflectionOct 28 1999The SU(2) invariant massive Thirring model with a boundary is considered on the basis of the vertex operator approach. The bosonic formulae are presented for the vacuum vector and its dual in the presence of the boundary. The integral representations ... More

Quantum Field Theory of Topological Defects as Inhomogeneous CondensatesOct 24 1999In the framework of the Closed-Time-Path formalism, we show how topological defects may arise in Quantum Field Theory as result of a localized (inhomogeneous) condensation of particles. We demonstrate our approach on two examples; kinks in the $2D \lambda ... More

Schlesinger transformations for elliptic isomonodromic deformationsOct 20 1999Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus ... More

Finite-gap difference opeators with elliptic coefficients and their spectral curvesOct 19 1999We review recent results on the finite-gap properties of difference operators with elliptic coefficients and give explicit characterization of spectral curves for difference analogues of the higher Lam\'e operators. This curve parametrizes double-Bloch ... More

N=2 Hamiltonians with sl(2) coalgebra symmetry and their integrable deformationsOct 18 1999Two dimensional classical integrable systems and different integrable deformations for them are derived from phase space realizations of classical $sl(2)$ Poisson coalgebras and their $q-$deformed analogues. Generalizations of Morse, oscillator and centrifugal ... More

Exact Solution of the Quantum Calogero-Gaudin System and of its q-DeformationOct 18 1999A complete set of commuting observables for the Calogero-Gaudin system is diagonalized, and the explicit form of the corresponding eigenvalues and eigenfunctions is derived. We use a purely algebraic procedure exploiting the co-algebra invariance of the ... More

Singularity confinement and algebraic entropy: the case of the discrete Painlevé equationsOct 18 1999We examine the validity of the results obtained with the singularity confinement integrability criterion in the case of discrete Painlev\'e equations. The method used is based on the requirement of non-exponential growth of the homogeneous degree of the ... More

Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systemsOct 15 1999Oct 27 1999The algebraic structure and the relationships between the eigenspaces of the Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are investigated through the Cherednik operators. We find an exact connection between the simultaneous ... More

Beyond Nonlinear Schrödinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range InteractionOct 15 1999Multi scales method is used to analyze a nonlinear differential-difference equation. In order $\epsilon^3$ the NLS equation is found to determine the space-time evolution of the leading amplitude. In the next order this has to satisfy a complex mKdV equation ... More

Lax pair, Darboux Transformations and solitonic solutions for a (2+1) dimensional NLSEOct 14 1999In this paper the Singular Manifold Method has allowed us to obtain the Lax pair, Darboux transformations and tau functions for a non-linear Schr\"odiger equation in 2+1 dimensions. In this way we can iteratively build different kind of solutions with ... More

Differential equations and integrable models: the SU(3) caseOct 13 1999Feb 07 2000We exhibit a relationship between the massless $a_2^{(2)}$ integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schr\"odinger equation. ... More

On integrable discretization of the inhomogeneous Ablowitz-Ladik modelOct 13 1999An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch oscillations are obtained. In particular, it is shown that ... More

Yang-Baxter Algebra for the n-Harmonic Oscillator Realisation of sp(2n,R)Oct 13 1999Using a rational R-matrix associated with the 4 x 4 defining matrix representation of c_2=sp(4), the Lie algebra of Sp(4), a one-site operator solution of the associated Yang-Baxter algebra acting in the Fock space of two harmonic oscillators is derived. ... More

The KdV equation on a half-lineOct 08 1999Nov 12 1999The initial boundary value problem on a half-line for the KdV equation with the boundary conditions $u|_{x=0}=a\leq0$, $u_{xx}|_{x=0}=3a^2$ is integrated by means of the inverse scattering method. In order to find the time evolution of the scattering ... More

Dispersionless Fermionic KdVOct 05 1999We analyze the dispersionless limits of the Kupershmidt equation, the SUSY KdV-B equation and the SUSY KdV equation. We present the Lax description for each of these models and bring out various properties associated with them as well as discuss open ... More

Calogero-Moser Models V: Supersymmetry and Quantum Lax PairOct 05 1999It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric and hyperbolic ... More

Matrix integrals and the geometry of spinorsSep 29 1999Apr 01 2001We obtain the collection of symmetric and symplectic matrix integrals and the collection of Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke, as specific elements in the Spin-group orbit of the vacuum vector of a fermionic ... More

Random Words, Toeplitz Determinants and Integrable Systems. ISep 28 1999It is proved that the limiting distribution of the length of the longest weakly increasing subsequence in an inhomogeneous random word is related to the distribution function for the eigenvalues of a certain direct sum of Gaussian unitary ensembles subject ... More

Evolution equations for quark-gluon distributions in multi-color QCD and open spin chainsSep 28 1999We study the scale dependence of the twist-3 quark-gluon parton distributions using the observation that in the multi-color limit the corresponding QCD evolution equations possess an additional integral of motion and turn out to be effectively equivalent ... More

Asymptotics of soliton solution for the perturbed Davey-Stewartson-1 equationsSep 26 1999Oct 16 1999The dromion of the Davey-Stewartson-1 equation is studied under perturbation on the large time.

On two aspects of the Painleve analysisSep 26 1999Mar 27 2013We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the singular expansions of its solutions around characteristic ... More

On a Schwarzian PDE associated with the KdV HierarchySep 24 1999We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy. In fact, this PDE can be considered as the generating ... More

Quasi-Lagrangian Systems of Newton EquationsSep 22 1999Systems of Newton equations of the form $\ddot{q}=-{1/2}A^{-1}(q)\nabla k$ with an integral of motion quadratic in velocities are studied. These equations generalize the potential case (when A=I, the identity matrix) and they admit a curious quasi-Lagrangian ... More

Dressing method and the coupled KP hierarchySep 22 1999The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by using the dressing method. It is shown that the coupled KP hierarchy can be reformulated as a reduced case of the 2-component KP hierarchy.

Orthogonal and symplectic matrix integrals and coupled KP hierarchySep 22 1999Orthogonal and symplectic matrix integrals are investigated. It is shown that the matrix integrals can be considered as a $\tau$-function of the coupled KP hierarchy, whose solution can be expressed in terms of pfaffians.

Boundary breathers in the sinh-Gordon modelSep 21 1999We present an investigation of the boundary breather states of the sinh-Gordon model restricted to a half-line. The classical boundary breathers are presented for a two parameter family of integrable boundary conditions. Restricting to the case of boundary ... More

Self-similarity in Spectral Problems and q-special FunctionsSep 21 1999Similarity symmetries of the factorization chains for one-dimensional differential and finite-difference Schr\"odinger equations are discussed. Properties of the potentials defined by self-similar reductions of these chains are reviewed. In particular, ... More

Self-similar solutions of NLS-type dynamical systemsSep 21 1999We study self-similar solutions of NLS-type dynamical systems. Lagrangian approach is used to show that they can be reduced to three canonical forms, which are related by Miura transformations. The fourth Painleve equation (PIV) is central in our consideration ... More

Conformal maps and dispersionless integrable hierarchiesSep 21 1999Mar 21 2000We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy singled out ... More

Soliton Solutions of Integrable Hierarchies and Coulomb PlasmasSep 21 1999Some direct relations between soliton solutions of integrable hierarchies and thermodynamical quantities of the Coulomb plasmas on the plane are revealed. We find that certain soliton solutions of the Kadomtsev-Petviashvili (KP) and B-type KP (BKP) hierarchies ... More

Surfaces of Constant negative Scalar Curvature and the Correpondence between the Liouvulle and the sine-Gordon EquationsSep 20 1999Nov 22 1999By studying the {\it internal} Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville, and the sine-Gordon equations. First, considering isometric immersions into the Lobachevskian plane, ... More

The complex Toda chains and the simple Lie algebras - solutions and large time asymptotics -- IISep 20 1999We propose a compact and explicit expression for the solutions of the complex Toda chains related to the classical series of simple Lie algebras g. The solutions are parametrized by a minimal set of scattering data for the corresponding Lax matrix. They ... More

The Structure of the Bazhanov-Baxter Model and a New Solution of the Tetrahedron EquationSep 20 1999We clarify the structure of the Bazhanov-Baxter model of the 3-dim N-state integrable model. There are two essential points, i) the cubic symmetries, and ii) the spherical trigonometry parametrization, to understand the structure of this model. We propose ... More

Vertex operators, semiclassical limit for soliton S-matrices and the number of bound states in Affine Toda Field TheoriesSep 18 1999Oct 05 1999Soliton time-delays and the semiclassical limit for soliton S-matrices are calculated for non-simply laced Affine Toda Field Theories. The phase shift is written as a sum over bilinears on the soliton conserved charges. The results apply to any two solitons ... More

Darboux transformations for a Bogoyavlenskii equation in 2+1 dimensionsSep 17 1999We use the singular manifold method to obtain the Lax pair, Darboux transformations and soliton solutions for a (2+1) dimensional integrable equation.

On the large time asymptotics of decaying Burgers turbulenceSep 16 1999Jul 16 2000The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and velocity differences ... More

Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring modelsSep 16 1999We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are ... More

Darboux Transformation for Supersymmetric KP HierarchiesSep 16 1999Jan 12 2000We construct Darboux transformations for the super-symmetric KP hierarchies of Manin--Radul and Jacobian types. We also consider the binary Darboux transformation for the hierarchies. The iterations of both type of Darboux transformations are briefly ... More

Finding and solving Calogero-Moser type systems using Yang-Mills gauge theoriesSep 16 1999Sep 21 1999Yang-Mills gauge theory models on a cylinder coupled to external matter charges provide powerful means to find and solve certain non-linear integrable systems. We show that, depending on the choice of gauge group and matter charges, such a Yang-Mills ... More

Discrete asymptotic nets and W-congruences in Plucker line geometrySep 16 1999Dec 11 2000The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the Lelieuvre-type representation ... More

The General Solution of the Complex Monge-Ampère Equation in a space of arbitrary dimensionSep 16 1999A general solution to the Complex Monge-Amp\`ere equation in a space of arbitrary dimensions is constructed.

The Complex Bateman Equation in a space of arbitrary dimensionSep 16 1999A general solution to the Complex Bateman equation in a space of arbitrary dimensions is constructed.

The General Solution of the Complex Monge-Ampère Equation in two dimensional spaceSep 16 1999The general solution to the Complex Monge-Amp\`ere equation in a two dimensional space is constructed.

The Complex Bateman EquationSep 16 1999The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special case.

Pfaff tau-functionsSep 15 1999Consider the evolution $$ \frac{\pl m_\iy}{\pl t_n}=\Lb^n m_\iy, \frac{\pl m_\iy}{\pl s_n}=-m_\iy(\Lb^\top)^n, $$ on bi- or semi-infinite matrices $m_\iy=m_\iy(t,s)$, with skew-symmetric initial data $m_{\iy}(0,0)$. Then, $m_\iy(t,-t)$ is skew-symmetric, ... More

The motion of a rigid body in a quadratic potential: an integrable discretizationSep 14 1999The motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n) x Symm(n). We give a Lagrangian derivation of the corresponding equations of motion, and ... More

Combinatorial R matrices for a family of crystals : C^{(1)}_n and A^{(2)}_{2n-1} casesSep 14 1999Sep 16 1999The combinatorial R matrices are obtained for a family {B_l} of crystals for U'_q(C^{(1)}_n) and U'_q(A^{(2)}_{2n-1}), where B_l is the crystal of the irreducible module corresponding to the one-row Young diagram of length l. The isomorphism B_l\otimes ... More

Lie point symmetries of integrable evolution equations and invariant solutionsSep 14 1999An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is applied to construct ... More