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

. 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 con...

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Bibliographic Details
Published in:European physical journal plus 2019-08, Vol.134 (8), p.380, Article 380
Main Authors: Yamgoué, Serge Bruno, Deffo, Guy Roger, Pelap, François Beceau
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Complex Systems
Condensed Matter Physics
Differential equations
Exact solutions
Mathematical and Computational Physics
Mathematical models
Molecular
Nonlinear differential equations
Optical and Plasma Physics
Partial differential equations
Physics
Physics and Astronomy
Polynomials
Rational functions
Regular Article
Solitary waves
Theoretical
Wave equations
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Summary:. 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.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/i2019-12733-8