The Lie-Symmetry Analysis Of (1+2)-coupled Nonlinear Schr(o|¨ )dinger Equations

The exact solutions of nonlinear partial differential equations will be of great significance in theory and applications, the solution can well explain some phenomena, such as vibration, and soliton propagation wave etc. The change of the spread of the sea waves, wind and other natural phenomena can set of nonlinear partial differential equations model, to make a study and solving these equations to better explain the phenomenon. Accurate solution of nonlinear partial differential equations is a good way to determine the quantitative relation between physical quantities, the exact solution of the graphics can be more intuitive response relationship between physical quantities.For a class of (1+2)-dimensional nonlinear Schrodinger equations, 8-dimensional subalgebra of the infinite Lie algebra is found and its one optimal system is constructed. By further reduction with its symmetry we obtain the corresponding ordinary differential equations. Solving the ordinary differential equations, one finds some exact invariant solutions of the Schrodinger equations.