Abstract.
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.
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Yamgoué, S.B., Deffo, G.R. & Pelap, F.B. A new rational sine-Gordon expansion method and its application to nonlinear wave equations arising in mathematical physics. Eur. Phys. J. Plus 134, 380 (2019). https://doi.org/10.1140/epjp/i2019-12733-8
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DOI: https://doi.org/10.1140/epjp/i2019-12733-8