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Zbl 1221.35338
Johnpillai, A.G.; Khalique, C.M.
Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 16, No. 3, 1207-1215 (2011). ISSN 1007-5704

Summary: 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.

MSC 2000:: *35Q53 KdV-like equations
35A30 Geometric theory for PDE, transformations

Keywords: modified KdV equation; solitons; Lie symmetries; optimal system; group-invariant solutions

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