SOLUTIONS AND LAWS OF CONSERVATION FOR COUPLED NONLINEAR SCHRODINGER-EQUATIONS - LIE GROUP-ANALYSIS

A set of two coupled nonlinear Schrodinger equations is systematically analyzed by means of Lie group technique. The physical situations und er consideration include nonlinear propagation in strongly birefringen t and multimode optical fibers. The most general Lie group of point sy mmetries, its Lie algebra, and a group of adjoint representations that correspond to the Lie algebra are identified. As a result, a complete list of group-invariant exact solutions is obtained and compared with earlier results. The corresponding laws of conservation are derived e mploying Noether's theorem.