Transformations from traveling wave (TW) solutions to non-TW solutions of evolution equations via a direct method

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Abstract

Studying properties of evolution equations arising in different physical contexts commonly starts from assuming the traveling wave (TW) solution form which reduces the problem to an ordinary differential equation (ODE). A variety of direct methods for finding such solutions have been designed but usually there is no algorithmic way to proceed further from this stage. In the present study, a method, which allows constructing non-traveling wave solutions of an evolution equation from known traveling wave solutions, is developed and applied to some types of equations. The transformations yielded by the method can be naturally used for finding new solutions of a given equation. Having the TW solutions (for example, solitary wave solutions) defined in an explicit form, more general non-TW solutions can be also explicitly determined. The transformations can also give insight into some general properties of the equations.

Original languageEnglish
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016
EditorsTheodore E. Simos, Theodore E. Simos, Charalambos Tsitouras
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735415386
DOIs
StatePublished - 21 Jul 2017
EventInternational Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016 - Rhodes, Greece
Duration: 19 Sep 201625 Sep 2016

Publication series

NameAIP Conference Proceedings
Volume1863
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016
Country/TerritoryGreece
CityRhodes
Period19/09/1625/09/16

Keywords

  • Classification of soliton equations
  • Integrability
  • KdV type equations
  • Multisoliton solutions
  • Solitons

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