Classical and Nonclassical Symmetry Classification of a Composite Type Equation

月星 白
2017 Pure Mathematics  
In this paper, the classifications of classical and nonclassical symmetries to a composite type equation 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 equations
more » ... ntial equations (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 corresponding 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.
doi:10.12677/pm.2017.74040 fatcat:hzvnb6ntnzfvjkn6jgapr55nxu