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http://dx.doi.org/10.11568/kjm.2015.23.1.11

TRAVELLING WAVE SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS  

Kim, Hyunsoo (Department of Mathematics Sungkyunkwan University)
Choi, Jin Hyuk (Humanitas College Kyung Hee University)
Publication Information
Korean Journal of Mathematics / v.23, no.1, 2015 , pp. 11-27 More about this Journal
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 at 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.
Keywords
Exact traveling wave solutions; Novikov equation; Qeng-Xue coupled equation; Generalized Riccati equation;
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