Hirota difference equation: inverse scattering transform, Darboux transformation, and solitons

DOI10.1007/s11232-014-0237-zzbMath1317.81252arXiv1407.0677OpenAlexW2470556444MaRDI QIDQ2352706

A. K. Pogrebkov

Publication date: 3 July 2015

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0677

zbMATH Keywords

inverse scattering transformsolitonDarboux transformationHirota difference equation

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Inverse scattering problems in quantum theory (81U40) Discrete version of topics in analysis (39A12) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)

Related Items (3)

Symmetries of the Hirota difference equation ⋮ Hirota difference equation and Darboux system: mutual symmetry ⋮ Spatio-Temporal Deformation of Kink-Breather to the (2+1)-Dimensional Potential Boiti–Leon–Manna–Pempinelli Equation

Cites Work

• Extended resolvent of the heat operator with a multisoliton potential
• Commutator identities on associative algebras and the integrability of nonlinear revolution equations
• Bäcklund transformations for the difference Hirota equation and the supersymmetric Bethe ansatz
• Elliptic solutions to difference nonlinear equations and related many-body problems
• Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation
• On Hirota's difference equations
• Towards an inverse scattering theory for non-decaying potentials of the heat equation
• Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
• Hirota difference equation and a commutator identity on an associative algebra
• 2D Toda chain and associated commutator identity
• Resolvent approach for the nonstationary Schrodinger equation
• Properties of solutions of the Kadomtsev–Petviashvili I equation
• Extended resolvent and inverse scattering with an application to KPI
• Constructing lump-like solutions of the Hirota–Miwa equation
• Generalized KP hierarchy: Möbius symmetry, symmetry constraints and Calogero-Moser system

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