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.


35Q53 KdV equations (Korteweg-de Vries equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
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