A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations |
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| Authors: | Zhiyong Zhang Yufu Chen |
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| Institution: | a KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR Chinab School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, PR China |
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| Abstract: | A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations is performed. First, complete infinite-order approximate symmetry classification of the equation is obtained by means of the method originated by Fushchich and Shtelen. An optimal system of one-dimensional subalgebras is derived and used to construct general formulas of approximate symmetry reductions and similarity solutions. Second, we study approximate homotopy symmetry of the equation and construct connections between the two symmetry methods for the first-order and higher-order cases, respectively. The series solutions derived by the two methods are compared. |
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| Keywords: | Approximate symmetry Optimal system Reduction Approximate homotopy symmetry |
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