Group classification and conservation laws of nonlinear filtration equation with a small parameter

•Group classification of perturbed nonlinear filtration equations is performed.•The nonlinearly self-adjoint perturbed equations are singled out.•Conservation laws are constructed for self-adjoint equations. Group classification of the perturbed nonlinear filtration equation is performed assuming th...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2014-02, Vol.19 (2), p.364-370
Main Authors: Alexandrova, A.A., Ibragimov, N.H., Lukashchuk, V.O.
Format: Article
Language:English
Subjects:
Approximation
Conservation laws
Nonlinear filtration
Nonlinear self-adjointness
Perturbed equation
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Summary:•Group classification of perturbed nonlinear filtration equations is performed.•The nonlinearly self-adjoint perturbed equations are singled out.•Conservation laws are constructed for self-adjoint equations. Group classification of the perturbed nonlinear filtration equation is performed assuming that the perturbation is an arbitrary function of the dependent variable. The nonlinear self-adjointness of the equation under consideration is investigated. Using these results, the approximate conservation laws are constructed.
ISSN:1007-5704
1878-7274
1878-7274
DOI:10.1016/j.cnsns.2013.06.012