Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations

Authors:
Bintao Cao
Affiliations:
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China 100190
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2010

Citing 2
Cited 0

Dynamics of director fields

SIAM Journal on Applied Mathematics
New kinks and solitons solutions to the (2+1) -dimensional Konopelchenko-Dubrovsky equation

Mathematical and Computer Modelling: An International Journal

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Abstract

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.