Partially nonclassical method and conformal invariance

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

Abstract

A generalization of the classical and nonclassical methods for finding similarity reductions of a partial differential equation (PDE), termed as the "partially nonclassical method", is developed. Applying the partially nonclassical method to the flat steady-state boundary layer (BL) equations shows that the partially nonclassical method enables one to obtain similarity reductions obtainable neither classical nor nonclassical methods. Based on the observation, that applying the classical Lie group method to a PDE yields transformations which do not leave the PDE invariant but modify it by a conformal factor, a unified representation of the classical, nonclassical and partially nonclassical methods for finding similarity reductions of PDEs is given. That representation may lead to further generalizations of the nonclassical method.

Original languageEnglish
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018
EditorsT.E. Simos, T.E. Simos, T.E. Simos, T.E. Simos, Ch. Tsitouras, T.E. Simos
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735418547
DOIs
StatePublished - 24 Jul 2019
EventInternational Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 - Rhodes, Greece
Duration: 13 Sep 201818 Sep 2018

Publication series

NameAIP Conference Proceedings
Volume2116
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018
Country/TerritoryGreece
CityRhodes
Period13/09/1818/09/18

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy (all)

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