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A new rational sine-Gordon expansion method and its application to nonlinear wave equations arising in mathematical physics

  • Serge Bruno YamgouéEmail author
  • Guy Roger Deffo
  • François Beceau Pelap
Regular Article
  • 44 Downloads

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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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Serge Bruno Yamgoué
    • 1
    Email author
  • Guy Roger Deffo
    • 2
  • François Beceau Pelap
    • 2
  1. 1.Department of Physics, Higher Teacher Training College BambiliThe University of BamendaBamendaCameroon
  2. 2.Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques (UR-2MSP), Faculté des SciencesUniversité de DschangDschangCameroon

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