Lie symmetry analysis, exact solutions, and conservation laws to multi-component nonlinear Schrodinger equations

The multi-component nonlinear Schrodinger equations (MNLS) are derived by extending the single-component nonlinear Schrodinger equation to multiple interacting fields. These equations often describe the dynamics of wave packets in quantum mechanics or nonlinear optics. In this paper, we investigate MNLS equations via the Lie symmetry method. The Lie infinitesimal symmetries of the MNLS equations are derived by solving recursive determining equations, and the symmetry reductions of the equations are given by using symmetry variables. Moreover, some interesting explicit solutions for the equations are constructed. Finally, the conservation laws of the MNLS equations are obtained utilizing Ibragimov's method with detailed derivation.

Automated summary

In this paper, the properties of the multi-component nonlinear Schrodinger equations (MNLS) are investigated using the Lie symmetry method. The symmetries and reductions of the equations are derived, and some explicit solutions as well as conservation laws are constructed.