Abstract
The Gardner equation with a variable-coefficient from fluid dynamics and plasma physics is investigated. Different kinds of solutions including breather-type soliton and two soliton solutions are obtained using bilinear method and extended homoclinic test approach. The proposed method can also be applied to solve other types of higher dimensional integrable and non-integrable systems.
Highlights
Many important phenomena in various fields can be describe by the nonlinear evolution equations
Seeking exact solutions of nonlinear partial differential equations is of great significance as it appears that these (NLPDEs) are mathematical models of complex physics phenomena arising in physics, mechanics, biology, chemistry and engineers
One of the most exciting advances of nonlinear science and theoretical physics has been a development of methods to look for exact solutions for nonlinear partial differential equations
Summary
Many important phenomena in various fields can be describe by the nonlinear evolution equations. Various powerful methods for obtaining explicit travelling solitary wave solutions to nonlinear equations have proposed such as [1,2,3,4,5,6,7,8]. One of the most exciting advances of nonlinear science and theoretical physics has been a development of methods to look for exact solutions for nonlinear partial differential equations. A search of directly seeking for exactly solutions of nonlinear equations has been more interest in recent years because of the availability of symbloic computation Mathematica or Maple. These computer systems allow us to perform some complicated and tedious algebraic and differential calculations on a computer.
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