99 research outputs found
Group classification of variable coefficient quasilinear reaction-diffusion equations
The group classification of variable coefficient quasilinear
reaction-diffusion equations is carried out exhaustively.
This became possible due to usage of a conditional equivalence group found in
the course of the study of admissible point transformation within the class.Comment: 10 pages, submitted to the Proceedings of the XVII Geometrical
Seminar (September 3-8, 2012, Zlatibor, Serbia
Group classification of variable coefficient KdV-like equations
The exhaustive group classification of the class of KdV-like equations with
time-dependent coefficients is carried out using
equivalence based approach. A simple way for the construction of exact
solutions of KdV-like equations using equivalence transformations is described.Comment: 8 pages; minor misprints are corrected. arXiv admin note: substantial
text overlap with arXiv:1104.198
Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach
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.Comment: 10 pages, minor change
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