Computational study for the conformable nonlinear Schrödinger equation with cubic–quintic–septic nonlinearities

Abstract

The fractional (3+1)-dimensional nonlinear Schrödinger equation with cubic–quintic–septic nonlinearities plays a significant role in the study of ultra-short pulses in highly nonlinear optical phenomena. The main purpose of this work is to determine the solution of (3+1)-dimensional nonlinear Schrödinger equation containing cubic–quintic–septic nonlinearities with conformal temporal operator. The solution of the considered problem is investigated using an adaptation of the residual power series method for the conformal fractional derivative. To illustrate the authenticity of the residual power series method to solve the nonlinear conformable Schrödinger equation with cubic–quintic–septic nonlinearities, three test applications are considered subject to different initial conditions. The variations of wave solutions of the applications corresponding to changes in the conformal derivative are depicted through graphical illustrations. The numerical comparisons confirm the accuracy of the presented results for the conformal (3+1)-dimensional nonlinear Schrödinger equation. The obtained results indicate the accuracy, suitability and competency of the residual power series method to examine other nonlinear conformable fractional differential equations arising in optics and other areas of physics.