Behavior of analytical schemes with non-paraxial pulse propagation to the cubic–quintic nonlinear Helmholtz equation

Abstract

In this paper, the cubic–quintic nonlinear Helmholtz equation which enables a pulse propagates in a planar waveguide with Kerr-like and quintic nonlinearities is studied. By noticing that the system is a non-integrable one, we could to get the diverse of solitary wave solutions by using standard tan(ϕ/2)-expansion technique and the exp(−Ω(η))-Expansion scheme. In particular, four forms of function solution including soliton, bright soliton, singular soliton, periodic wave solutions are investigated. To achieve this, an illustrative example of the Helmholtz equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The effect of the free parameters on the behavior of acquired figures to some solutions of two nonlinear exact cases was also analyzed due to the nature of nonlinearities. The dynamic properties of the obtained results are shown and analyzed by some density, two and three-dimensional images. We believe that our results will be a way for future research generating optical memories based on the non-paraxial solitons.