Abstract
Abstract This paper studies the Kudryashov-Sinelshchikov and Jimbo-Miwa equations. Subsequently, we formally derive the dark (topological) soliton solutions for these equations. By using the sine-cosine method, some additional periodic solutions are derived. The physical parameters in the soliton solutions of the ansatz method, amplitude, inverse width and velocity, are obtained as functions of the dependent model coefficients. PACS Codes:02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fg.
Highlights
In recent years, many powerful methods to construct exact solutions of nonlinear partial differential equations have been established and developed, which led to one of the most exciting advances of nonlinear science and theoretical physics
In Section, we give the description of the sine-cosine method and we apply this method to the Kudryashov-Sinelshchikov (KS) and Jimbo-Miwa equations
4 Conclusion In this paper, the KS and Jimbo-Miwa equation (JM) equations are solved by the sine-cosine method as well as by the solitary wave ansatz method
Summary
Many powerful methods to construct exact solutions of nonlinear partial differential equations have been established and developed, which led to one of the most exciting advances of nonlinear science and theoretical physics. Many kinds of exact soliton solutions have been obtained by using, for example, the tanh-sech method [ – ], extended tanh method [ – ], homogeneous balance method [ , ], first integral method [ , In Section , we give the description of the sine-cosine method and we apply this method to the Kudryashov-Sinelshchikov (KS) and Jimbo-Miwa equations.
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