Reduction Operators and Exact Solutions of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities
Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
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Academic Editor: Roman M. Cherniha
Symmetry 2017, 9(1), 3; https://doi.org/10.3390/sym9010003
Received: 13 October 2016 / Revised: 13 December 2016 / Accepted: 14 December 2016 / Published: 22 December 2016
(This article belongs to the Special Issue Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models)
Reduction operators, i.e., the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities, are investigated within the framework of a singular reduction operator. A classification of regular reduction operators is performed with respect to generalized extended equivalence groups. Exact solutions of some nonlinear wave models, which are invariant under certain reduction operators, are also constructed.
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Keywords:
symmetry analysis; reduction operators; equivalence group; nonlinear wave equation; exact solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Huang, D.; Zhu, Y.; Yang, Q. Reduction Operators and Exact Solutions of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities. Symmetry 2017, 9, 3. https://doi.org/10.3390/sym9010003
AMA Style
Huang D, Zhu Y, Yang Q. Reduction Operators and Exact Solutions of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities. Symmetry. 2017; 9(1):3. https://doi.org/10.3390/sym9010003
Chicago/Turabian StyleHuang, Dingjiang; Zhu, Yan; Yang, Qinmin. 2017. "Reduction Operators and Exact Solutions of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities" Symmetry 9, no. 1: 3. https://doi.org/10.3390/sym9010003
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