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Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients

✍ Scribed by A.G. Johnpillai; C.M. Khalique

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 214 KB
Volume: 16
Category: Article
ISSN: 1007-5704
DOI: 10.1016/j.cnsns.2010.06.025

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✦ Synopsis

This paper studies the modified Korteweg-de Vries equation with time variable coefficients of the damping and dispersion using Lie symmetry methods. We carry out Lie group classification with respect to the time-dependent coefficients. Lie point symmetries admitted by the mKdV equation for various forms for the time variable coefficients are obtained. The optimal system of one-dimensional subalgebras of the Lie symmetry algebras are determined. These are then used to determine exact group-invariant solutions, including soliton solutions, and symmetry reductions for some special forms of the equations.

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