Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation

doi:10.1007/s10483-015-1910-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (3): 365-378.doi: https://doi.org/10.1007/s10483-015-1910-6

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Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation

Yinshan YUN¹, Chaolu TEMUER²

1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China;
2. College of Arts and Sciences, Shanghai Maritime University, Shanghai 200135, China

Received:2013-08-12 Revised:2014-07-04 Online:2015-03-01 Published:2015-03-01
Contact: Chaolu TEMUER E-mail:tmchaolu@shmtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11071159 and 11301259), the Shanghai Key Projects (No. 12510501700), the Scientific Research of College of Inner Mongolia (No.NJZZ14053), and the Natural Science Foundation of Inner Mongolia (Nos. 2013MS0105 and 2014MS0114)

Abstract

Abstract: A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.

Key words: symmetry classification, classical symmetry, nonclassical symmetry, nonlinear wave equation

2010 MSC Number:

Yinshan YUN;Chaolu TEMUER. Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 365-378.

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Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation

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