The \(N\)-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation).
type: Item
instance of: scholarly article
title: The \(N\)-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation).
zbMATH Open document ID: 1048.35104
DOI: 10.1016/S0960-0779(02)00314-4
author: A. J. Morrison
author: E. J. Parkes
published in: Chaos, Solitons and Fractals
publication date: 2004-01-14T00:00:00Z
review text: The goal of this paper is to present a generalization of the Vakhnenko equation, namely \[ {\partial\over\partial x} (D^2u+ qu^2+\beta u)+ qDu= 0,\quad D:= {\partial\over\partial t}+ u{\partial\over\partial x}, \] where \(\beta\) and \(q\) are arbitrary nonzero constants, and to find its \(N\)-soliton solution. The authors find not only loop soliton solutions, but himp-line and cusp-like soliton solutions.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37K40
zbMATH DE Number: 2027073
zbMATH Keywords: \(N\)-soliton solution
zbMATH Keywords: generalized Vakhnenko equation
zbMATH Keywords: Hirota's method
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2027073