Abstract
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
Highlights
The study of autonomous nonlinear evolution equations has a rich and long history, which has continued to attract attention in more recent years
Searching for exact traveling wave solutions to nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena in many fields such as fluid dynamics, water wave mechanics, meteorology, electromagnetic theory, plasma physics and nonlinear optics
The aim of this work is to demonstrate the efficiency of the generalized Kudryashov method for finding exact traveling wave solutions transmutable to the solitary wave solutions for system of nonlinear evolution equations
Summary
The study of autonomous nonlinear evolution equations has a rich and long history, which has continued to attract attention in more recent years. Searching for exact traveling wave solutions to nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena in many fields such as fluid dynamics, water wave mechanics, meteorology, electromagnetic theory, plasma physics and nonlinear optics. The aim of this work is to demonstrate the efficiency of the generalized Kudryashov method for finding exact traveling wave solutions transmutable to the solitary wave solutions for system of nonlinear evolution equations. For this purpose, we consider the one dimensional variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations
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