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Korteweg-de Vries-Burgers equation with a higher-order nonlinearity

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Abstract

In this paper, we study a Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. An asymptotic analysis of proper traveling wave solutions is presented by means of the qualitative theory of differential equations. An approximate solution with arbitrary velocity is obtained by using the Adomian decomposition method, which agrees well with the phase plane analysis. A class of solitary wave solutions is also derived which covers existing traveling wave solutions in the literature.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas-Pan American, Edinburg, TX, 78539, USA

    Zhaosheng Feng

  2. Department of Mathematics, Texas A& M University, College Station, TX, 77843, USA

    Indranil Sen Gupta

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  1. Zhaosheng Feng
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  2. Indranil Sen Gupta
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Correspondence to Zhaosheng Feng.

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Feng, Z., Gupta, I.S. Korteweg-de Vries-Burgers equation with a higher-order nonlinearity. Differ Equ Dyn Syst 16, 3–27 (2008). https://doi.org/10.1007/s12591-008-0002-6

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