2013•International Journal of Advanced Mathematical SciencesOpen access

Travelling wave solutions of the generalized Zakharov-Kuznetsov equation via the extended generalized Riccati equation mapping method

Olusola Tosin Kolebaje, Pelumi Akinyemi, Michael Obende

Abstract

Exact hyperbolic, trigonometric and rational travelling wave solutions to the (2+1)-dimensional Generalized Zakharov-Kuznetsov (GZK) equation via the extended generalized Riccati equation mapping method are presented in this paper. The twenty one travelling wave solutions obtained were verified by putting them back into the GZK equation with the aid of Mathematica. This shows that the extended generalized Riccati equation mapping method is a powerful tool for finding exact solution to nonlinear partial differential equations in physics, mathematics and other applications.

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Key concepts: Riccati equation, Mathematics, Algebraic Riccati equation, Trigonometry, Partial differential equation, Traveling wave, First-order partial differential equation, Wave equation