On the conservation laws and invariant solutions of the mKdV equation

Yasar E.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.363, no.1, pp.174-181, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 363 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.1016/j.jmaa.2009.08.030
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.174-181
  • Keywords: Conservation laws, Symmetries, PARTIAL-DIFFERENTIAL-EQUATIONS, SYMMETRIES, WATER
  • Bursa Uludag University Affiliated: Yes

Abstract

In this paper, we consider modified Korteweg-de Vries (mKdV) equation. By using the nonlocal conservation theorem method and the partial Lagrangian approach, conservation laws for the mKdV equation are presented. It is observed that only nonlocal conservation theorem method lead to the nontrivial and infinite conservation laws. In addition, invariant solution is obtained by utilizing the relationship between conservation laws and Lie-point symmetries of the equation. (C) 2009 Elsevier Inc. All rights reserved.