A Procedure to Construct Conservation Laws of Nonlinear Evolution Equations


YAŞAR E. , SAN S.

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, vol.71, no.5, pp.475-480, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 5
  • Publication Date: 2016
  • Doi Number: 10.1515/zna-2016-0057
  • Title of Journal : ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
  • Page Numbers: pp.475-480

Abstract

In this article, we established abundant local conservation laws to some nonlinear evolution equations by a new combined approach, which is a union of multiplier and Ibragimov's new conservation theorem method. One can conclude that the solutions of the adjoint equations corresponding to the new conservation theorem can be obtained via multiplier functions. Many new families of conservation laws of the Pochammer-Chree (PC) equation and the Kaup-Boussinesq type of coupled KdV system are successfully obtained. The combined method presents a wider applicability for handling the conservation laws of nonlinear wave equations. The conserved vectors obtained here can be important for the explanation of some practical physical problems, reductions, and solutions of the underlying equations.