一类复合方程的古典与非古典对称分类.pdfVIP

Pure Mathematics 理论数学, 2017, 7(4), 301-309 Published Online July 2017 in Hans. /journal/pm /10.12677/pm.2017.74040 Classical and Nonclassical Symmetry Classification of a Composite Type Equation Yuexing Bai, Bilige Sudao* College of Sciences, Inner Mongolia University of Technology, Hohhot Inner Mongolia th th th Received: Jun. 25 , 2017; accepted: Jul. 9 , 2017; published: Jul. 19 , 2017 Abstract In this paper, the classifications of classical and nonclassical symmetries to a composite type equ- ation are determined. Firstly, the classification of classical symmetries to the composite equation is determined based on the differential characteristic set algorithm. Secondly, the classification of nonclassical symmetries for the composite equation is determined. First step, adding invariant surface condition and the original equation composed a new system of partial differential equa- tions (PDEs), and the determining equations (DTEs) of symmetry to PDEs are determined by using the symbolic computation software Mathematica. Second step, the nonclassical symmetries are classified by calculating DTEs, so we can obtain the specific form of F(u) which is the parameter of the composite equation. Third step, the invariant solutions and exact solutions of the correspond- ing nonclassical symmetry are determined. The invariant solutions and exact solutions cannot be obtained by classical symmetry, so enrich the exact solutions of the composite equation. Keywords Classical Symmetry, Nonclassical Symmetry, Symmetry Classification, Differential Characteristic Set Algorithm, The Composite Equation 一类复合方程的古典和非古典对称分类 白月星，苏道毕力格* 内蒙古工业大学理学院，内蒙古 呼和浩特 收稿日期：2017年6月25 日；录用日期：2017年7月9 日；发布日