Single and multi-solitary wave solutions to a class of nonlinear evolution equations

By Deng‐Shan Wang, Hongbo Li. 2008

71 citations recorded by the source corpus.

Abstract In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa–Holm equation, Kolmogorov–Petrovskii–Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the ( 2 + 1 ) -dimensional asymmetric version of the Nizhnik–Novikov–Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f59d1f8b899643c669d5c40d47288b52eefbccbd

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation (2019, methodology): “The KPP equation is studied through distinct techniques like the discrimination algorithm [36], the (G’/G)-expansion method [37], the homotopy perturbation method (HMP) [23], the generalized two-dimensional differential transform method [24], and many others [22,38–42].”