Nonlinear interaction of solitary waves described by multi-rational wave solutions of the \((2+1)\)-dimensional Kadomtsev-Petviashvili equation with variable coefficients. (English) Zbl 1372.35067
Summary: In this paper, the generalized unified method is used to construct multi-rational wave solutions of the \((2 + 1)\)-dimensional Kadomtsev-Petviashvili equation with variable coefficients. This is an extension of the previous work that was given by the same author in [the author and H. I. Abdel-Gawad, “Multi-wave solutions of the \((2+1)\)-dimensional Nizhnik-Novikov-Veselov equations with variable coefficients”, Eur. Phys. J. Plus 130, No. 10, Article ID 215, 11 p. (2015; doi:10.1140/epjp/i2015-15215-1)]. The \((2+1)\)-dimensional Kadomtsev-Petviashvili equation with variable coefficients can be used to characterize many nonlinear phenomena in fluid dynamics, plasma physics and some other nonlinear science when the inhomogeneities of media and non-uniformities of boundaries are taken into consideration. To give more physical insight into the obtained solutions, we present graphically their representative structures by setting the arbitrary functions in the solutions as specific functions. Moreover, the influences of the variable coefficient functions and interaction properties of solitary waves are discussed for physical interests and possible applications.
Keywords:
generalized unified method; variable coefficients; the \((2+1)\)-dimensional Kadomtsev-Petviashvili equation; multi-rational solutionsReferences:
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