Equations of Geodesic Deviation and the Inverse Scattering TransformSolutions of equations of geodesic deviation in three- and four- dimensional spaces obtained by the inverse scattering transform are considered. It is shown that in the case of three-dimensional…Vadim V. Varlamov·May 24, 2004SaveLearn
Polarization scattering by soliton-soliton collisionsCollision of two solitons of the Manakov system is analytically studied. Existence of a complete polarization mode switching regime is proved and the parameters of solitons prepared for polarization…V. S. Shchesnovich·Dec 9, 2003SaveLearn
On the bilinear equations for Fredholm determinants appearing in random matricesIt is shown how the bilinear differential equations satisfied by Fredholm determinants of integral operators appearing as spectral distribution functions for random matrices may be deduced from the…J. Harnad·Jun 17, 2003SaveLearn
Airy Kernel and Painleve IIWe prove that the distribution function of the largest eigenvalue in the Gaussian Unitary Ensemble (GUE) in the edge scaling limit is expressible in terms of Painlevé II. Our goal is to concentrate…Craig A. Tracy, Harold Widom·Nov 25, 2000SaveLearn
p-adic Difference-Difference Lotka-Volterra Equation and Ultra-Discrete LimitIn this article, we have studied the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We pointed out that the structure of the space given by…Shigeki Matsutani·Jan 9, 2000SaveLearn
On the Miura map between the dispersionless KP and dispersionless modified KP hierarchiesWe 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.…Jen-Hsu Chang, Ming-Hsien Tu·Dec 29, 1999SaveLearn
Vector NLS hierarchy solitons revisited: dressing transformation and tau function approachWe discuss some algebraic aspects of the integrable vector non-linear Schrödinger hierarchies (GNLSr). These are hierarchies of zero-curvature equations constructed from affine Kac-Moody…Harold Blas·Dec 27, 1999SaveLearn
Vertex operator solutions to the discrete KP-hierarchyVertex 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…Mark Adler, Pierre van Moerbeke·Dec 23, 1999SaveLearn
Singular solution of the Liouville equation under perturbationSmall 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…L. A. Kalyakin·Dec 22, 1999SaveLearn
Whitham-Toda Hierarchy in the Laplacian Growth ProblemThe 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…Mark Mineev-Weinstein, Anton Zabrodin·Dec 18, 1999SaveLearn
Liouville equation under perturbationSmall 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.L. A. Kalyakin·Dec 16, 1999SaveLearn
Real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspacesThree 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…Olaf Lechtenfeld, Alexander Sorin·Dec 15, 1999SaveLearn
Quantum Lax Pair From Yang-Baxter EquationsWe 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…A. Lima-Santos·Dec 14, 1999SaveLearn
The Pfaff lattice, Matrix integrals and a map from Toda to PfaffWe 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,…M. Adler, P. van Moerbeke·Dec 6, 1999SaveLearn
Dynamical Symmetry Approach to Periodic HamiltoniansWe 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…Hui Li, Dimitri Kusnezov·Dec 6, 1999SaveLearn
Group Theoretical Properties and Band Structure of the Lame HamiltonianWe 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…Hui Li, Dimitri Kusnezov, Francesco Iachello·Dec 6, 1999SaveLearn
Generalized KP hierarchy: Möbius Symmetry, Symmetry Constraints and Calogero-Moser SystemAnalytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that Möbius symmetry transformation for the singular…L. V. Bogdanov, B. G. Konopelchenko·Dec 6, 1999SaveLearn
Integrable Couplings of Soliton Equations by Perturbations I. A General Theory and Application to the KdV HierarchyA 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…Wen-Xiu Ma·Dec 3, 1999SaveLearn
N=4 Sugawara construction on affine sl(2|1), sl(3) and mKdV-type superhierarchiesThe 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…E. Ivanov, S. Krivonos, F. Toppan·Nov 30, 1999SaveLearn
Quantum Lax scheme for Ruijsenaars modelsWe 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…Branislav Jurco, Peter Schupp·Nov 26, 1999SaveLearn
Construction of variable mass sine-Gordon and other novel inhomogeneous quantum integrable modelsThe 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…Anjan Kundu·Nov 26, 1999SaveLearn
Surfaces of Constant negative Scalar Curvature and the Correpondence between the Liouvulle and the sine-Gordon EquationsBy studying the 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,…H. Belich, G. Cuba, R. Paunov·Nov 22, 1999SaveLearn
Equations and Integrals of Motion in Discrete Integrable Ak-1 Algebra ModelsWe 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,…A. P. Protogenov, V. A. Verbus·Nov 19, 1999SaveLearn
Multidimensional analogs of geometric s<-->t dualityThe 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…I. G. Korepanov·Nov 18, 1999SaveLearn
Separation of variables for soliton equations via their binary constrained flowsBinary constrained flows of soliton equations admitting 2× 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…Yunbo Zeng, Wen-Xiu Ma·Nov 17, 1999SaveLearn