Darboux transformation and the explicit solutions of differential- difference and difference-difference evolution equations. I

DOI10.1007/BF00405296zbMath0421.35001OpenAlexW2037002589MaRDI QIDQ1133053

Vladimir B. Matveev

Publication date: 1979

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00405296

zbMATH Keywords

Darboux transformationexplicit solutions of differential-difference and difference-difference evolution equationsZakharov-Schabat equations

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Initial value problems for linear higher-order PDEs (35G10) Solutions to PDEs in closed form (35C05) Higher-order parabolic equations (35K25)

Related Items (35)

Darboux and binary Darboux transformations for discrete integrable systems. II: Discrete potential mKdV equation ⋮ On the existence of Darboux transformations for banded matrices ⋮ New solitary wave solutions for two nonlinear evolution equations ⋮ Integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell ⋮ Wronskian addition formula and Darboux-Pöschl-Teller potentials ⋮ Intertwine operators and elementary Darboux transforms in differential rings and modules ⋮ On the Darboux transformations and sequences of \(p\)-orthogonal polynomials ⋮ Darboux transformations for orthogonal differential systems and differential Galois theory ⋮ Darboux transformations on a space scale ⋮ Generalizations of the finite nonperiodic Toda lattice and its Darboux transformation ⋮ Some comments on the rational solutions of the Zakharov-Schabat equations ⋮ Extensions and generalizations of lattice Gelfand-Dickey hierarchy ⋮ Differential-difference evolution equations. II: Darboux transformation for the Toda lattice ⋮ Discrete Crum's theorems and lattice KdV-type equations ⋮ Multisoliton solutions of integrable discrete and semi-discrete principal chiral equations ⋮ Transformations of matricial \({\alpha}\)-Stieltjes non-negative definite sequences ⋮ The \(n\)-fold Darboux transformation for the Kundu-Eckhaus equation and dynamics of the smooth positon solutions ⋮ Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP hierarchy ⋮ Lax Pair, Binary Darboux Transformation and New Grammian Solutions of Nonisospectral Kadomtsev–Petviashvili Equation with the Two-Singular-Manifold Method ⋮ Mixed lump-soliton solutions of the \((3+1)\)-dimensional soliton equation ⋮ Prototype and reduced nonlinear integrable lattice systems with the modulated pulson behavior ⋮ Binary Darboux Transformation and Quasideterminant Solutions of The Chiral Field ⋮ Explicit Solutions to an Integrable Lattice ⋮ Darboux transformation of a semi-discrete coupled dispersionless integrable system ⋮ Darboux transformations of Jacobi matrices and Padé approximation ⋮ Darboux transformations for non-Abelian and nonlocal equations of the Toda lattice type ⋮ A new two-parameter family of exactly solvable Dirac Hamiltonians ⋮ A binary Darboux transformation for the Toda lattice ⋮ Semi-discrete integrable nonlinear Schrödinger system with background-controlled inter-site resonant coupling ⋮ Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters ⋮ Nonlinear integrable model of Frenkel-like excitations on a ribbon of triangular lattice ⋮ Darboux transformation and two-dimensional Toda lattice ⋮ Darboux transformation and exact solutions for two dimensional \(A_{2n -1}^{(2)}\) Toda equations ⋮ Darboux transformation of the second-type derivative nonlinear Schrödinger equation ⋮ Solitons of the Korteweg-de Vries equation on the background of a known solution

Cites Work

• Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
• Unnamed Item

This page was built for publication: Darboux transformation and the explicit solutions of differential- difference and difference-difference evolution equations. I