Open AccessDifferential invariants and group classification of variable coefficient generalized Gardner equation
Author(s) -
Guo Mei-Yu,
Gao Jie
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.6686
Subject(s) - korteweg–de vries equation , mathematics , constant coefficients , equivalence (formal languages) , infinitesimal , variable coefficient , differential equation , variable (mathematics) , nonlinear system , group (periodic table) , constant (computer programming) , equivalence class (music) , mathematical analysis , pure mathematics , physics , quantum mechanics , computer science , programming language
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.