Comparison of approximate symmetry and approximate homotopy symmetry to the Cahn–Hilliard equation

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摘要

Complete infinite order approximate symmetry and approximate homotopy symmetry classifications of the Cahn–Hilliard equation are performed and the reductions are constructed by an optimal system of one-dimensional subalgebras. Zero order similarity reduced equations are nonlinear ordinary differential equations while higher order similarity solutions can be obtained by solving linear variable coefficient ordinary differential equations. The relationship between two methods for different order are studied and the results show that the approximate homotopy symmetry method is more effective to control the convergence of series solutions than the approximate symmetry one.

论文关键词:Approximate symmetry,Approximate homotopy symmetry,Reduction,Cahn–Hilliard equation

论文评审过程:Received 1 July 2010, Revised 12 May 2012, Available online 27 July 2012.

论文官网地址:https://doi.org/10.1016/j.cam.2012.07.016