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Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach. (English) Zbl 1245.35114
Summary: Group classification of classes of mKdV-like equations with time-dependent coefficients is carried out. The usage of equivalence transformations appears to be a crucial point for the exhaustive solution of the problem. We prove that all the classes under consideration are normalized. This allows us to formulate the classification results in three ways: up to two kinds of equivalence (which are generated by transformations from the corresponding equivalence groups and all admissible point transformations) and using no equivalence. A simple way for the construction of exact solutions of mKdV-like equations using equivalence transformations is described.
35Q53KdV-like (Korteweg-de Vries) equations
35A22Transform methods (PDE)
35B06Symmetries, invariants, etc. (PDE)
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