The sub-ODE method and soliton solutions for a higher order dispersive cubic–quintic nonlinear Schrödinger equation

Based on the subsidiary ordinary differential equation method, we derive some new exact analytic soliton solutions for a higher order dispersive cubic–quintic nonlinear Schrödinger equation that describes the propagation of femtosecond pulses in nonlinear optical fibers. These kinds of solutions may be useful to explain some physical phenomena related to wave propagation in a nonlinear Schrödinger system supporting high-order nonlinear and dispersive effects.