Group Classification and Exact Solutions of a Class of Variable Coefficient Nonlinear Wave Equations
HUANG Ding-Jiang1, MEI Jian-Qin2, ZHANG Hong-Qing2
1Department of Mathematics, East China University of Science and Technology, Shanghai 2002372Department of Applied Mathematics, Dalian University of Technology, Dalian 116024
Group Classification and Exact Solutions of a Class of Variable Coefficient Nonlinear Wave Equations
HUANG Ding-Jiang1, MEI Jian-Qin2, ZHANG Hong-Qing2
1Department of Mathematics, East China University of Science and Technology, Shanghai 2002372Department of Applied Mathematics, Dalian University of Technology, Dalian 116024
摘要Complete group classification of a class of variable coefficient (1+1)-dimensional wave equations is performed. The possible additional equivalence transformations between equations from the class under consideration and the conditional equivalence groups are also investigated. These allow simplification of the results of the classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of special forms of these equations via the classical Lie method. Nonclassical symmetries of the wave equations are discussed.
Abstract：Complete group classification of a class of variable coefficient (1+1)-dimensional wave equations is performed. The possible additional equivalence transformations between equations from the class under consideration and the conditional equivalence groups are also investigated. These allow simplification of the results of the classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of special forms of these equations via the classical Lie method. Nonclassical symmetries of the wave equations are discussed.
HUANG Ding-Jiang;MEI Jian-Qin;ZHANG Hong-Qing. Group Classification and Exact Solutions of a Class of Variable Coefficient Nonlinear Wave Equations[J]. 中国物理快报, 2009, 26(5): 50202-050202.
HUANG Ding-Jiang, MEI Jian-Qin, ZHANG Hong-Qing. Group Classification and Exact Solutions of a Class of Variable Coefficient Nonlinear Wave Equations. Chin. Phys. Lett., 2009, 26(5): 50202-050202.
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