Symmetry and Integrability of Equations of Mathematical Physics − 2011
Olena Vaneeva (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)
Group classification of variable-coefficient mKdV equations
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.
The results are published in [Olena Vaneeva, Lie symmetries and exact solutions of
variable coefficient mKdV equations: an equivalence based approach, Commun. Nonlinear Sci. Numer. Simulat. 17 (2012) 611-618].