Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.
Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）-...Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.展开更多
Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by no...Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.展开更多
文摘Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.
基金supported by the Natural Science Foundation of Shandong Province of China under Grant Nos.Q2005A01
文摘Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.
基金The project supported by National Natural Science Foundation of China under Grant No. 10071033, the Natural Science Foundation of Jiangsu Province under Grant No. BK2002003, the Project of Technology Innovation Plan for Postgraduate of Jiangsu Province in Year 2006 under Grant No. 72, and the Natural Science Directed Foundation of the Jiangsu Higher Education Institutions under Grant No. 06KJDll0001
文摘Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.
