A multiplicity result for the generalized Kadomtsev-Petviashvili equation
type: Item
instance of: scholarly article
title: A multiplicity result for the generalized Kadomtsev-Petviashvili equation
zbMATH Open document ID: 0902.35100
DOI: 10.12775/TMNA.1996.012
published in: Topological Methods in Nonlinear Analysis
publication date: 1998-11-09T00:00:00Z
review text: The authors consider the problem of uniqueness of weak solitary-wave solutions to the (generally, nonintegrable) equation \[ u_t+u_{xxx} + f'(u)\cdot u_x=D_x^{-1}u_{yy}. \] The solitary wave is sought for in the form \(u(x,y,t) = u(x - ct,y)\), \(c\) being the velocity of its motion along the \(x\) axis. The solutions of this type are looked for as stationary points of the corresponding Hamiltonian. The main result is a proof of the fact that, under certain conditions imposed on the function \(f(u)\) in the equation (essentially, a class of power functions \(f(u) \sim u^p\) with \(p\) = const is considered), the equation has, at least, \textit{two} geometrically distinct weak solitary-wave solutions. The proof is based on the use of the techniques of the Lyusternik - Schnirelman theory for stationary points of the Hamiltonian.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 1127673
zbMATH Keywords: solitary wave
zbMATH Keywords: Lyusternik - Schnirelman theory
zbMATH Keywords: uniqueness
author: Zhi-Qiang Wang
author: Michel Willem
reviewed by: B. A. Malomed
MaRDI profile type: Publication
full work available at URL: tmna.1996.012
OpenAlex ID: W2603677457
description: scientific article; zbMATH DE number 1127673