Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations

Details Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations

2009-02-19

arxiv.org/abs/0902.3308v1

Physics

Mathematical Physics

27 pages

Scientific paper

The Jimbo-Miwa equation is the second equation in the well known KP hierarchy of integrable systems, which is used to describe certain interesting (3+1)-dimensional waves in physics but not pass any of the conventional integrability tests. The Konopelchenko-Dubrovsky equations arose in physics in connection with the nonlinear weaves with a weak dispersion. In this paper, we obtain two families of explicit exact solutions with multiple parameter functions for these equations by using Xu's stable-range method and our logarithmic generalization of the stable-range method. These parameter functions make our solutions more applicable to related practical models and boundary value problems.

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