Conservation Laws and Soliton Solutions of the (1+1)-Dimensional Modified Improved Boussinesq Equation


GÜNER Ö., SAN S., BEKİR A., YAŞAR E.

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, vol.70, no.8, pp.669-672, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 8
  • Publication Date: 2015
  • Doi Number: 10.1515/zna-2015-0172
  • Title of Journal : ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
  • Page Numbers: pp.669-672
  • Keywords: Conservation Laws, Exact Solution, Modified Improved Boussinesq Equation, Multiplier Method, Partial Lagrangian Approach, NONLINEAR EVOLUTION-EQUATIONS, TRAVELING-WAVE SOLUTIONS, TANH-FUNCTION METHOD, DIFFERENTIAL-EQUATIONS, BLOW-UP, SYMMETRIES, EXISTENCE, BRIGHT

Abstract

In this work, we consider the (1+1)-dimensional modified improved Boussinesq (IMBq) equation. As the considered equation is of evolution type, no recourse to a Lagrangian formulation is made. However, we showed that by utilising the partial Lagrangian method and multiplier method, one can construct a number of local and nonlocal conservation laws for the IMBq equation. In addition, by using a solitary wave ansatz method, we obtained exact bright soliton solutions for this equation. The parameters of the soliton envelope (amplitude, widths, velocity) were obtained as function of the dependent model coefficients. Note that, it is always useful and desirable to construct exact solutions especially soliton-type envelope for the understanding of most nonlinear physical phenomena.