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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 8
  • Publication Date: 2015
  • Doi Number: 10.1515/zna-2015-0172
  • Journal Name: ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • 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
  • Bursa Uludag University Affiliated: Yes

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.