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 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.