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Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients. (English) Zbl 1221.35338
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.

35Q53KdV-like (Korteweg-de Vries) equations
35A30Geometric theory for PDE, characteristics, transformations
Full Text: DOI
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