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Exact Solutions to Nonlinear Schrödinger Equation and Higher-Order Nonlinear Schrödinger Equation

We study solutions of the nonlinear Schrödinger equation (NLSE) and higher-order nonlinear Schrödinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained.