Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach

Olena Vaneeva

doi:10.1016/j.cnsns.2011.06.038

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arXiv · 1104.1981

Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach

Olena Vaneeva

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Abstract

Group classification of classes of mKdV-like equations with time-dependent coefficients is carried out. The usage of equivalence transformations appears 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 of the construction of exact solutions of mKdV-like equations using equivalence transformations is described.

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Olena Vaneeva. 2011-04-11. Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach. https://doi.org/10.1016/j.cnsns.2011.06.038

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