Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 17, Issue 2, Pages 611-618Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2011.06.038
Keywords
Lie symmetries; Group classification; mKdV equation; Equivalence group
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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. (C) 2011 Elsevier B.V. All rights reserved.
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