Lie Symmetry Group, Invariant Subspace, and Conservation Law for the Time-Fractional Derivative Nonlinear Schrödinger Equation

Abstract

In this paper, a time-fractional derivative nonlinear Schrödinger equation involving the Riemann–Liouville fractional derivative is investigated. We first perform a Lie symmetry analysis of this equation, and then derive the reduced equations under the admitted optimal-symmetry system. Moreover, with the invariant subspace method, several exact solutions for the equation and their figures are presented. Finally, the new conservation theorem is applied to construct the conservation laws of the equation.

Keywords

• time-fractional derivative nonlinear Schrödinger equation
• symmetry group
• invariant subspace
• conservation law