Weak asymptotics method and the interaction of infinitely narrow \(\delta\)-solitons.
type: Item
instance of: scholarly article
title: Weak asymptotics method and the interaction of infinitely narrow \(\delta\)-solitons.
zbMATH Open document ID: 1040.35092
DOI: 10.1016/S0362-546X(03)00104-4
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-07-30T00:00:00Z
review text: The authors consider a KdV-type equation of the form \[ u_t+(u^m)_x + \varepsilon^2u_{xxx}=0, \] where \(m\geq2\) is integer, \(\varepsilon\to+0\) is a small parameter. The interaction of solitons for the equation is studied. It is proposed some general procedure (the weak asymptotics method) for describing the interaction of nonlinear waves in both the integrable (\(m=2,3\)) and nonintegrable (\(m>3\)) cases. A suitable definition of the weak asymptotic solution is given in the paper.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37K40
Mathematics Subject Classification ID: 35G25
zbMATH DE Number: 1957315
zbMATH Keywords: KdV-type equation
zbMATH Keywords: small dispersion
zbMATH Keywords: interaction of solitons
zbMATH Keywords: weak asymptotics method
zbMATH Keywords: weak asymptotic solution
author: V. G. Danilov
author: Georgii A. Omel'yanov
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1957315