From conservation laws of generalized Schrödinger equations to exact solutions

Algorithm for finding exact solutions for the generalized nonlinear Schrödinger equations is presented. The key point of our approach is the use of conservation laws for nonlinear partial differential equations, from which the first integrals of ordinary differential equations are found. The obtained first integrals using this approach make it possible to construct analytical solutions of the initial generalized nonlinear partial differential equations. Taking into account the traveling wave reduction for the two conservation laws in this paper this approach is applied for finding exact solutions of the three generalized nonlinear Schrödinger equations.