A new rational sine-Gordon expansion method and its application to nonlinear wave equations arising in mathematical physics
Department of Physics, Higher Teacher Training College Bambili, The University of Bamenda, P.O. Box 39, Bamenda, Cameroon
2 Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques (UR-2MSP), Faculté des Sciences, Université de Dschang, BP 69, Dschang, Cameroon
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Accepted: 6 May 2019
Published online: 7 August 2019
In this paper, a novel approach for constructing exact solutions to nonlinear partial differential equations is presented. The method is designed to be a generalization of the well-known sine-Gordon expansion since it is based on the use of the sine-Gordon equation as an auxiliary equation. In contrast to the classic sine-Gordon expansion method, it involves a more general ansatz that is a rational function, rather than a polynomial one, of the solutions of the auxiliary equation. This makes the approach introduced capable of capturing more exact solutions than that standard sine-Gordon method. Two important mathematical models arising in nonlinear science, namely, the (2 + 1)-dimensional generalized modified Zakharov-Kuznetsov equation and the (2 + 1) -Dimensional Broer-Kaup-Kupershmidt (BKK) system are used to illustrate the applicability, the simplicity, and the power of this method. As a result, we successfully obtain some solitary solutions that are known in the literature as well as other new soliton and singular soliton solutions.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019