A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such no...A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.展开更多
Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve ...Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve a large system of determining equations,which seems rather difficult to solve,then the differential form Wu's method is used to decompose the determining equations into a series of equations,which are easy to solve.To illustrate the usefulness of this method,we apply it to some test problems,and the results show the performance of the present work.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11071159 and11301259)the Shanghai Key Projects(No.12510501700)+1 种基金the Scientific Research of College of Inner Mongolia(No.NJZZ14053)the Natural Science Foundation of Inner Mongolia(Nos.2013MS0105and 2014MS0114)
文摘A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.
基金National Natural Science Foundation of China(No.61862048)。
文摘Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve a large system of determining equations,which seems rather difficult to solve,then the differential form Wu's method is used to decompose the determining equations into a series of equations,which are easy to solve.To illustrate the usefulness of this method,we apply it to some test problems,and the results show the performance of the present work.
