Lax pairs and Bäcklund transformations for a coupled Ramani equation and its related system
type: Item
instance of: scholarly article
title: Lax pairs and Bäcklund transformations for a coupled Ramani equation and its related system
zbMATH Open document ID: 0983.37086
DOI: 10.1016/S0893-9659(00)00052-5
author: Xing-Biao Hu
author: Dao-Liu Wang
author: Hon-Wah Tam
published in: Applied Mathematics Letters
publication date: 2000-11-16T00:00:00Z
review text: The authors deal with the following coupled Ramani equation of the form \[ u_{xxxxxx}+ 15u_{xx}u_{xxx} +15u_xu_{xxxx} +45u_x^2u_{xx} -5(u_{xxxt} +3u_{xx}u_t +3u_xu_{xt}) -5u_{tt}+ 18w_x=0 \] \[ w_t-w_{xxx}- 3w_xu_x-3wu_{xx} =0. \] The authors show that this system is integrable in the sense of having a Bäcklund transformation and Lax pairs. Soliton solutions and rational solutions are also obtained.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 37K15
Mathematics Subject Classification ID: 37K35
zbMATH DE Number: 1531195
reviewed by: Messoud Efendiev
describes a project that uses: Mathematica
MaRDI profile type: Publication
cites work: A higher-order water-wave equation and the method for solving it.
cites work: Mathematics of dispersive water waves
cites work: Coupled KdV equations with multi-Hamiltonian structures
cites work: Solitons and infinite dimensional Lie algebras
cites work: Q3733558
cites work: Theory of a Solid State Plasma Waveguide in a Transverse Magnetic Field
cites work: Bilinear transformation method
cites work: A direct method for dromion solutions of the Davey-Stewartson equations and their asymptotic properties
cites work: Q5289006
Recommended article: Bilinear Bäcklund transformation and Lax pair for a coupled Ramani equation
Recommended article: Bäcklund transformations and Lax pairs for two differential-difference equations
Recommended article: Lax pairs, Backlund transformations and special solutions for ordinary differential equations
Recommended article: Bäcklund transformation and Lax pair for an extended integrable differential-difference system
Recommended article: Bäcklund transformation, Lax pair, and solutions for the Caudrey–Dodd–Gibbon equation
Recommended article: Q5413482
Recommended article: Bäcklund transformation and Lax representation for a nonlinear differential equation
Recommended article: Q4472784
Recommended article: Q2992865
Recommended article: Bäcklund transformation and special solutions for the Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations
description: scientific article; zbMATH DE number 1531195