Abstract
In this present paper, the Fan sub-equation method is used to construct exact traveling wave solutions of the (1 + 1) dimensional Kaup-Kupershmidt equation. Many exact traveling wave solutions are successfully obtained, which contain solitary wave solutions, trigonometric function solutions, hyperbolic function solutions and Jacobian elliptic function periodic solutions with double periods.
Highlights
Nonlinear partial differential equations are widely used to describe complex phenomena in vary scientific fields and especially in areas of physics such as plasma, fluid mechanics, biology, solid state physics, nonlinear optics and so on
The investigation of the exact solutions to nonlinear equations plays an important role in the study of nonlinear science
Many powerful methods to seek for exact solutions to the nonlinear differential equations have been proposed
Summary
Nonlinear partial differential equations are widely used to describe complex phenomena in vary scientific fields and especially in areas of physics such as plasma, fluid mechanics, biology, solid state physics, nonlinear optics and so on. The important feature of Fan’ method is to, without much extra effort and without considering the integrability of nonlinear equations, directly get a series of exact solutions in a uniform way, which cover all results of tanh function method, extended function method, F-expansion method, etc. This method is a powerful technique to symbolically compute traveling wave solutions of nonlinear evolution equations and is widely used by many researcher such as in [15,16,17] and by the references therein. We will use the Fan sub-equation method to discuss the (1+1) dimensional Kaup-Kupershmidt equation [18] which can be shown in the form ut
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