Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK＇s direct method, we build the relationship between new solutions and old ones and the （3＋1）-d...Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK＇s direct method, we build the relationship between new solutions and old ones and the （3＋1）-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the （3＋1）-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.展开更多
In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its...In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its sister equation, the （2＋1）-dimensional coupled derivative nonlinear Schrodinger equation, are shown to describe 3-h.s, The （2 ＋ 1 ）-dimensional generalized HF model：St=（1/2i[S,Sy]＋2iσS）x,σx=-1/4i tr（SSxSy）, in which S ∈ GLc（2）/GLc（1）×GLc（1）,provides another example of （2＋1）-dimensional differential equations describing 3-h.s. As a direct con-sequence, the geometric construction of an infinire number of conservation lairs of such equations is illustrated. Furthermore we display a new infinite number of conservation lairs of the （2＋1）-dimensional nonlinear Schrodinger equation and the （2＋1）-dimensional derivative nonlinear Schrodinger equation by a geometric way.展开更多
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004zx16 tCorresponding author, E-maih zzlh100@163.com
文摘Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK＇s direct method, we build the relationship between new solutions and old ones and the （3＋1）-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the （3＋1）-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.
基金The project partially supported by National Natural Science Foundation of China
文摘In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its sister equation, the （2＋1）-dimensional coupled derivative nonlinear Schrodinger equation, are shown to describe 3-h.s, The （2 ＋ 1 ）-dimensional generalized HF model：St=（1/2i[S,Sy]＋2iσS）x,σx=-1/4i tr（SSxSy）, in which S ∈ GLc（2）/GLc（1）×GLc（1）,provides another example of （2＋1）-dimensional differential equations describing 3-h.s. As a direct con-sequence, the geometric construction of an infinire number of conservation lairs of such equations is illustrated. Furthermore we display a new infinite number of conservation lairs of the （2＋1）-dimensional nonlinear Schrodinger equation and the （2＋1）-dimensional derivative nonlinear Schrodinger equation by a geometric way.
