New types of multisoliton solutions of some integrable equations via direct methods

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Exact explicit solutions, which describe new multisoliton dynamics, have been identified for some KdV type equations using direct methods devised for this purpose. It is found that the equations, having multi-soliton solutions in terms of the KdV-type solitons, possess also an alternative set of multi-soliton solutions which include localized static structures that behave like (static) solitons when they collide with moving solitons. The alternative sets of solutions include the steady-state solution describing the static soliton itself and unsteady solutions describing mutual interactions in a system consisting of a static soliton and several moving solitons. As distinct from common multisoliton solutions those solutions represent combinations of algebraic and hyperbolic functions and cannot be obtained using the traditional methods of soliton theory.

Original languageEnglish
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015
EditorsTheodore E. Simos, Theodore E. Simos, Charalambos Tsitouras, Theodore E. Simos
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413924
DOIs
StatePublished - 8 Jun 2016
EventInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015 - Rhodes, Greece
Duration: 23 Sep 201529 Sep 2015

Publication series

NameAIP Conference Proceedings
Volume1738
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015
Country/TerritoryGreece
CityRhodes
Period23/09/1529/09/15

Keywords

  • Generalized Kaup-Kupershmidt Solitons
  • Integrability
  • KdV type equations
  • Multisoliton solutions
  • Static solitons

ASJC Scopus subject areas

  • General Physics and Astronomy

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