Soliton solutions of the resonant nonlinear Schrödinger equation using modified auxiliary equation method with three different nonlinearities

Abstract

The dynamical behavior of the resonant nonlinear Schrödinger equation is investigated in this paper. Resonant nonlinear Schrödinger equation describes the wave propagation in fiber optics. The modified auxiliary equation method is used to extract the soliton solutions of resonant nonlinear Schrödinger equation. The modified auxiliary equation method is novel, stable and efficient exact method. This equation is considered with Kerr law, parabolic law and anti-cubic law of nonlinearities. Many novel soliton solutions such as periodic, dark, bell shaped and singular soliton solutions are extracted using the proposed method. The 3D graphs and 2D contour graphs of retrieved solutions are plotted using symbolic software, Maple. The obtained results containing trigonometric function, hyperbolic function and rational functions are hopped to be beneficial to understand the dynamical framework of the related physical phenomena.