Linear integral equations and nonlinear difference-difference equations
From MaRDI portal
Publication:1079774
DOI10.1016/0378-4371(84)90059-1zbMath0598.45009OpenAlexW2087578966MaRDI QIDQ1079774
Publication date: 1984
Published in: Physica A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0378-4371(84)90059-1
nonlinear Schrödinger equationBäcklund transformationsKorteweg-de Vries equationsine-Gordon equationBianchi identitiesHeisenberg spin chainGel'fand-Levitan equationintegrable nonlinear difference-difference equationsinverse-scattering transform
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Partial functional-differential equations (35R10) Euler-Poisson-Darboux equations (35Q05) Integral equations with miscellaneous special kernels (45H05)
Related Items (62)
INTEGRABLE DISCRETIZATIONS FOR LATTICE SYSTEM: LOCAL EQUATIONS OF MOTION AND THEIR HAMILTONIAN PROPERTIES ⋮ An integrable semi-discretization of the Boussinesq equation ⋮ Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps ⋮ On the Lagrangian formulation of multidimensionally consistent systems ⋮ Properties of the non-autonomous lattice sine-Gordon equation: consistency around a broken cube property ⋮ Darboux and binary Darboux transformations for discrete integrable systems. II: Discrete potential mKdV equation ⋮ The direct linearizing transform for three-dimensional lattice equations ⋮ Lax pair for the Adler (lattice Krichever-Novikov) system ⋮ The discrete Korteweg-de Vries equation ⋮ Infinitesimal Darboux transformation and semi-discrete MKDV equation ⋮ Iteration of some discretizations of the nonlinear Schrödinger equation ⋮ Solutions to ABS Lattice Equations via Generalized Cauchy Matrix Approach ⋮ Discrete nonlinear hyperbolic equations. Classification of integrable cases ⋮ Jacobi elliptic function solutions of the Ablowitz-Ladik discrete nonlinear Schrödinger system ⋮ Integrable dynamics of a discrete curve and the Ablowitz–Ladik hierarchy ⋮ Integrability conditions for nonautonomous quad-graph equations ⋮ Fredholm determinants and the mKdV/Sinh-Gordon hierarchies ⋮ Linear integral equations, infinite matrices, and soliton hierarchies ⋮ Reduction groups and related integrable difference systems of nonlinear Schrödinger type ⋮ On a Two-Parameter Extension of the Lattice KdV System Associated with an Elliptic Curve ⋮ On a coupled Kadomtsev–Petviashvili system associated with an elliptic curve ⋮ Integrable discretization and numerical simulation for the Ito equation ⋮ Periodic discrete Darboux transforms ⋮ Large deviations for Ablowitz-Ladik lattice, and the Schur flow ⋮ On the fourth-order lattice Gel'fand-Dikii equations ⋮ Lattice equations, hierarchies and Hamiltonian structures ⋮ Linear integral equations and multicomponent nonlinear integrable systems. I ⋮ Complete integrability and singularity confinement of nonautonomous modified Korteweg-de Vries and sine Gordon mappings ⋮ Discrete analogues for two nonlinear Schrödinger type equations ⋮ Lattice equations, hierarchies and Hamiltonian structures. II: KP-type of hierarchies on 2D lattices ⋮ Lattice equations, hierarchies and Hamiltonian structures. III: The 2D Toda and KP hierarchies ⋮ Linear integral equations and multicomponent nonlinear integrable systems. II ⋮ Discrete Toda field equations ⋮ Multidimensional quadrilateral lattices are integrable. ⋮ On an integrable discretization of the modified Korteweg-de Vries equation. ⋮ Integrable discretization of nonlinear Schrödinger equation and its application with Fourier pseudo-spectral method ⋮ A semi-discrete modified KdV equation ⋮ Direct Linearization of Extended Lattice BSQ Systems ⋮ Reduction of quad-equations consistent around a cuboctahedron I: Additive case ⋮ Cauchy problem for integrable discrete equations on quad-graphs ⋮ Discretization of nonlinear evolution equations over associative function algebras ⋮ Integrable discretization of soliton equations via bilinear method and Bäcklund transformation ⋮ Solitons of some nonlinear sigma-like models ⋮ Linearizing integral transform for the multicomponent lattice KP ⋮ Generalized lattice Heisenberg magnet model and its quasideterminant soliton solutions ⋮ Integrable discretizations of the Euler top ⋮ Preface. Special issue in honor of Reinout Quispel ⋮ \(k\)-integrals and \(k\)-Lie symmetries in discrete dynamical systems ⋮ A discrete negative AKNS equation: generalized Cauchy matrix approach ⋮ Integrable mappings and soliton equations ⋮ Integrable mappings and soliton equations. II ⋮ Integrability of reductions of the discrete Korteweg–de Vries and potential Korteweg–de Vries equations ⋮ Solitons of the (2+2)-dimensional Toda lattice ⋮ On the equivalence of the discrete nonlinear Schrödinger equation and the discrete isotropic Heisenberg magnet ⋮ Discrete potential Ablowitz–Kaup–Newell–Segur equation ⋮ A variational perspective on continuum limits of ABS and lattice GD equations ⋮ Do integrable mappings have the Painlevé property? ⋮ A new family of four-dimensional symplectic and integrable mappings ⋮ An alternating integrable map whose square is the QRT map ⋮ Numerical evaluations of periodic wave solutions, integrable time discretization and their applications to the mKdV–sine-Gordon equation ⋮ Yang–Baxter maps, Darboux transformations, and linear approximations of refactorisation problems ⋮ Discrete power functions on a hexagonal lattice I: derivation of defining equations from the symmetry of the Garnier system in two variables
Cites Work
- Unnamed Item
- Unnamed Item
- Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
- Bäcklund transformations, the inverse scattering method, solitons, and their applications. NSF research workshop on contact transformations
- On some linear integral equations generating solutions of nonlinear partial differential equations
- Bäcklund transformations and nonlinear differential difference equations
- Nonlinear differential difference equations as Backlund transformations
- The inverse scattering transform: Semi-infinite interval
- Nonlinear differential–difference equations and Fourier analysis
- A complete solution of the periodic Toda problem
- On the Solution of a Class of Nonlinear Partial Difference Equations
- On the Toda Lattice. II: Inverse-Scattering Solution
This page was built for publication: Linear integral equations and nonlinear difference-difference equations
