Enhanced group classification of Gardner equations with time-dependent coefficients
Abstract
We classify the Lie symmetries of variable coefficient Gardner equations (called also the combined KdV-mKdV equations). In contrast to the particular results presented in Molati and Ramollo (2012) we perform the exhaustive group classification. It is shown that the complete result can be achieved using either the gauging of arbitrary elements of class by the equivalence transformations or the method of mapping between classes. As by-product of the second approach the complete group classification of a class of variable coefficient mKdV equations with forcing term is derived. Advantages of the use of the generalized extended equivalence group in comparison with the usual one are also discussed.
Cite
@article{arxiv.1407.8488,
title = {Enhanced group classification of Gardner equations with time-dependent coefficients},
author = {Olena Vaneeva and Oksana Kuriksha and Christodoulos Sophocleous},
journal= {arXiv preprint arXiv:1407.8488},
year = {2015}
}
Comments
12 pages; the version published in Commun. Nonlinear Sci. Numer. Simulat