Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-04-11
Commun Nonlinear Sci Numer Simulat 17 (2012) 611-618
Nonlinear Sciences
Exactly Solvable and Integrable Systems
10 pages, minor changes
Scientific paper
10.1016/j.cnsns.2011.06.038
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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