Original scientific paper
Exact solutions of the mKdV equation with time-dependent coefficients
Andrew Gratien Johnpillai
; nternational Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, South Africa
Chaudry Masood Khalique
; nternational Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, South Africa
Anjan Biswas
; Department of Mathematical Sciences,Delaware State University, Dover, U.S.A.
Abstract
In this paper, we study the time variable coefficient modified
Korteweg-de Vries (mKdV) equation from group-theoretic point of
view. We obtain Lie point symmetries admitted by the mKdV equation
for various forms for the time variable coefficients. We use the
symmetries to construct the group-invariant solutions for each of
the cases of the arbitrary variable coefficients. Finally, the
solitary wave ansatz will be used to carry out the integration of
the mKdV equation that will be supported by a concrete example.
Keywords
modified KdV equation; solutions; lie point symmetries; group-invariant solutions
Hrčak ID:
74896
URI
Publication date:
21.12.2011.
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