Painlevé analysis, auto-Bäcklund transformation and new analytic solutions for a generalized variable-coefficient Korteweg-de Vries (KdV) equation

Guang-Mei Wei (), Yi-Tian Gao (), Wei Hu and Chun-Yi Zhang

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 53, issue 3, 343-350

Abstract: There has been considerable interest in the study on the variable-coefficient nonlinear evolution equations in recent years, since they can describe the real situations in many fields of physical and engineering sciences. In this paper, a generalized variable-coefficient KdV (GvcKdV) equation with the external-force and perturbed/dissipative terms is investigated, which can describe the various real situations, including large-amplitude internal waves, blood vessels, Bose-Einstein condensates, rods and positons. The Painlevé analysis leads to the explicit constraint on the variable coefficients for such a equation to pass the Painlevé test. An auto-Bäcklund transformation is provided by use of the truncated Painlevé expansion and symbolic computation. Via the given auto-Bäcklund transformation, three families of analytic solutions are obtained, including the solitonic and periodic solutions. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 05.45.Yv Solitons; 02.30.Jr Partial differential equations; 52.35.Mw Nonlinear phenomena: waves; wave propagation; and other interactions (including parametric effects; mode coupling; ponderomotive effects; etc.); 47.35.+i Hydrodynamic waves (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1140/epjb/e2006-00378-3

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