Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao zbMATH Openarrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1983
Data sources: zbMATH Open
Journal of Mathematical Physics
Article . 1983 . Peer-reviewed
Data sources: Crossref
versions View all 2 versions
addClaim

A particle representation for Korteweg–de Vries solitons

A particle representation for Korteweg-de Vries solitons
Authors: Bowtell, Graham; Stuart, Allen E. G.;

A particle representation for Korteweg–de Vries solitons

Abstract

In an earlier paper we established an equivalence between the dynamics of interacting sine–Gordon solitons and the motions of poles of the corresponding Hamiltonian density. In particular, we found analytic expressions for the forces acting between the solitons and used these to represent the N-soliton solution as an N-body interaction between classical particles. In this paper, we apply the methods of our previous analysis to obtain a dynamically equivalent particle representation for interacting Korteweg–de Vries solitons. The representation is faithful and a detailed analysis is present for the one- and two-soliton solutions. In these cases the particle motions accurately reflect the behavior of the solitons, giving, respectively, a uniform motion and a repulsive interaction. Furthermore, in the case of the two-soliton solutions, the phase shifts calculated from the particle trajectories are the same as those obtained from an asymptotic analysis of the waveforms. Because of the nature of the Korteweg–de Vries equation, there are important differences between the present analysis and that employed for the sine–Gordon equation and these are discussed in some detail. A comparison with related work on other solutions of the Korteweg–de Vries is also presented.

Related Organizations
Keywords

classical many-body problems with two-body forces, duality between fields, Partial differential equations of mathematical physics and other areas of application, Constructive quantum field theory, nonlinear evolution equations, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, particle representation, Korteweg-de Vries solitons, kinematics of the poles

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    20
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
20
Average
Top 10%
Top 10%
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!