Korean J. Math. Vol. 23 No. 1 (2015) pp.11-27
DOI: https://doi.org/10.11568/kjm.2015.23.1.11

Travelling wave solutions for some nonlinear evolution equations

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Published: Mar 30, 2016
Keywords:
Exact traveling wave solutions, Novikov equation, Qeng- Xue coupled equation, Generalized Riccati equation.
Mathematics Subject Classification:
35Q92.

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Hyunsoo Kim
Department of Mathematics Sungkyunkwan University Suwon 440-746, Republic of Korea
Jin Hyuk Choi
Humanitas College Kyung Hee University Yongin 446-701, Republic of Korea

Abstract

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a flat bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.


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