Remarks on several 2+1 dimensional lattices

DOI10.1063/1.1430899zbMath1061.37059OpenAlexW2046262970MaRDI QIDQ4830721

Hon-Wah Tam, Xian-Min Qian, Xing-Biao Hu

Publication date: 14 December 2004

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

Full work available at URL: https://doi.org/10.1063/1.1430899

zbMATH Keywords

soliton solutionsvariable transformationsdifferential-difference KP equationintegrable propertiescoupled bilinear equations\(2+1\) dimensional latticeshigher-dimensional generalization

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Discrete version of topics in analysis (39A12) Lattice dynamics; integrable lattice equations (37K60)

Related Items (12)

New type of source extension for a two-dimensional special lattice equation and determinant solutions ⋮ Commutativity of Pfaffianization and Bäcklund transformations for a special two-dimensional lattice ⋮ One variant of a \((2+1)\)-dimensional Volterra system and its \((1+1)\)-dimensional reduction ⋮ A special two-dimensional lattice by Blaszak and Szum: solitons, breathers, lump solutions, and their interactions and dynamics ⋮ Periodic solutions to a coupled two-dimensional lattice presented by Blaszak and Szum with Riemann-theta function ⋮ Lax pairs and conservation laws for two differential-difference systems ⋮ Duality of positive and negative integrable hierarchies via relativistically invariant fields ⋮ On an integrable two-dimensional special lattice with self-consistent sources ⋮ The applications of the gauge transformation for the BKP hierarchy ⋮ Darboux transformation and explicit solutions for the derivative versions of Toda equation ⋮ A differential-difference Kadomtsev-Petviashvili family possesses a common Kac-Moody-Virasoro symmetry algebra ⋮ Two integrable differential-difference equations derived from the discrete BKP equation and their related equations

Cites Work

• Construction of higher local (2 + 1) dimensional exponential lattice equations
• Lie algebraic approach to the construction of (2+1)-dimensional lattice-field and field integrable Hamiltonian equations
• Method for Generating Discrete Soliton Equations. IV
• New integrable differential-difference systems
• Wronskian and rational solutions of the differential-difference KP equation
• A new integrable differential-difference system and its explicit solutions
• From the special 2 + 1 Toda lattice to the Kadomtsev-Petviashvili equation

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