Bäcklund transformation, non-local symmetry and exact solutions for \((2+1)\)-dimensional variable coefficient generalized KP equations
type: Item
instance of: scholarly article
title: Bäcklund transformation, non-local symmetry and exact solutions for \((2+1)\)-dimensional variable coefficient generalized KP equations
zbMATH Open document ID: 0962.37038
DOI: 10.1016/S1007-5704(00)90021-2
author: Zhenya Yan
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2001-06-19T00:00:00Z
review text: The author deals with \((2+1)\)-dimensional variable coefficient KP equations which is the integrable model \[ G(u)\equiv u_{xt}+ h_1 (u_{xxx}+ 6uu_x+ 6h_3 u_x)_x+ h_2 u_{yy}- (h_3+ 12 h_1 h_3^2)= 0, \] where \(h_1= h_1(t)\), \(h_2= h_2(t)\) and \(h_3= h_3(t)\) are arbitrary functions of \(t\). Recently, improving the homogeneous balance method the author applied it to KdV, KP, variable coefficient KdV and \((2+1)\)-dimensional KPP equations. Here the author extends the method to \((2+1)\)-dimensional variable coefficient generalized KP equations. As a result, a Bäcklund transformation and a nonlocal symmetry are found. Then by using the Bäcklund transformation, six families of exact solutions for \((2+1)\)-dimensional variable coefficient KP equations are obtained, which contain new soliton-like solutions.
Mathematics Subject Classification ID: 37K35
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 37K30
zbMATH DE Number: 1471946
zbMATH Keywords: integrable model
zbMATH Keywords: Bäcklund transformation
zbMATH Keywords: nonlocal symmetry
zbMATH Keywords: generalized KP equation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q3995225
cites work: Painlevé property, auto-Bäcklund transformation, Lax pairs, and reduction to the standard form for the Korteweg–De Vries equation with nonuniformities
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cites work: Exact solutions for a compound KdV-Burgers equation
cites work: New exact solutions to a solutions to a system of coupled KdV equations
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description: scientific article; zbMATH DE number 1471946