Admissible equivalence transformations for linearization of nonlinear wave type equations

Özer S. S.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.16, pp.5522-5534, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 16
  • Publication Date: 2019
  • Doi Number: 10.1002/mma.5465
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5522-5534
  • Istanbul Technical University Affiliated: Yes

Abstract

In the present paper, we consider a general family of two-dimensional wave equations, which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated the existence problem of point transformations that lead mappings between linear and nonlinear members of particular families and determined the structure of the nonlinear terms of linearizable equations. We have also given examples about some equivalence transformations between linear and nonlinear equations and obtained exact solutions of nonlinear equations via the linear ones.