In this article, the resonance nonlinear Schrödinger equation is studied, which elucidates the propagation of one-dimensional long magnetoacoustic waves in a cold plasma, dynamic of solitons and Madelung fluids in various nonlinear systems. The Lie symmetry analysis is used to achieve the invariant solution and similarity reduction of the resonance nonlinear Schrödinger equation. The infinitesimal generators, symmetry groups, commutator table and adjoint table have been obtained by the aid of invariance criterion of Lie symmetry. Also, one-dimensional system of subalgebra is constructed with the help of adjoint representation of a Lie group on its Lie algebra. By one-dimensional optimal subalgebra, the main equations are reduced to ordinary differential equations and their invariant solutions are provided. The general conservation theorem has been used to establish a set of non-local and non-trivial conservation laws.
A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws
