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New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative

This paper considers the generalized nonlinear Schrödinger (GNLS) equation with group velocity dispersion and second-order spatio-temporal dispersion coefficients. We obtain new dispersive solutions of a variety of GNLS equations via the exponential rational function method with the local M-derivative of order [Formula: see text]. The results obtained demonstrate that the employed method is simple and quite efficient for constructing exact solutions for other nonlinear equations arising in mathematical physics and nonlinear optics.