Bell-polynomial manipulations on the Bäcklund transformations and Lax pairs for some soliton equations with one Tau-function

DOI10.1063/1.3504168zbMath1314.35129OpenAlexW2227779206MaRDI QIDQ5254863

Pan Wang, Xing Lü, Bo Tian, Kun Sun

Publication date: 10 June 2015

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

Full work available at URL: https://doi.org/10.1063/1.3504168

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Polynomial solutions to PDEs (35C11)

Related Items (22)

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Cites Work

• Unnamed Item
• Unnamed Item
• Symbolic computation on cylindrical-modified dust-ion-acoustic nebulons in dusty plasmas
• Soliton-like solutions for a \((2+1)\)-dimensional generalization of the shallow water wave equations.
• Exact solutions for some nonlinear evolution equations which describe pseudo-spherical surfaces
• Soliton equations and simple combinatorics
• Multisoliton solutions in terms of double Wronskian determinant for a generalized variable-coefficient nonlinear Schrödinger equation from plasma physics, arterial mechanics, fluid dynamics and optical communications
• Bäcklund transformations and their applications
• On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations
• Exponential polynomials
• Reply to: ``Comment on: `Spherical Kadomtsev-Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation' [Phys. Lett. A 361 (2007) 520]
• N-Soliton Solutions of Model Equations for Shallow Water Waves
• Painleve property and pseudopotentials for nonlinear evolution equations
• New similarity reductions of the Boussinesq equation
• MULTI-SOLITON SOLUTIONS AND THEIR INTERACTIONS FOR THE (2+1)-DIMENSIONAL SAWADA-KOTERA MODEL WITH TRUNCATED PAINLEVÉ EXPANSION, HIROTA BILINEAR METHOD AND SYMBOLIC COMPUTATION
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions
• A wave equation in 2+1: Painleve analysis and solutions
• The construction of exact solutions of two-dimensional integrable generalizations of Kaup-Kuperschmidt and Sawada-Kotera equations via \(\overline \partial\)-dressing method

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