Differential invariants and group classification of variable coefficient generalized Gardner equation

Guo Mei-Yu; Gao Jie

doi:10.7498/aps.58.6686

Abstract
By using Lie’s invariance infinitesimal criterion, we obtain the continuous equivalence transformations of a class of nonlinear Gardner equations with variable coefficients. Starting from the equivalence algebra， we construct the differential invariants of order one and make group classification. Finally some general class of variable coefficient nonlinear Gardner equations can be mapped to constant-coefficient mKdV equation and KdV-mKdV equation. In particular, some exact solutions of the Gardner equation with variable coefficients are obtained.

Keywords:
Lie’s invariance infinitesimal criterion /

differential invariants /

group classification /

variable coefficient generalized Gardner equation
Authors and contacts
Guo Mei-Yu,

Gao Jie

1.
聊城大学数学科学学院,聊城 252059
References

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Vol. 58, Issue 10 - 2009-05-20

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Differential invariants and group classification of variable coefficient generalized Gardner equation

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