Nonparaxial pulse propagation to the cubic–quintic nonlinear Helmholtz equation

Abstract

In this paper, we study the cubic–quintic nonlinear Helmholtz equation which enables a pulse propagating with Kerr-like and quintic properties further spatial dispersion. By noticing that the system is a nonintegrable one, we could get variety forms of solitary wave solutions by using a generalized [Formula: see text]-expansion method. In particular, we investigate four forms of the function solutions including soliton, bright soliton, singular soliton, periodic wave solutions. To perform this, the demonstrative pattern of the Helmholtz equation is made to show the probability and dependability of the protocol utilized in this research. The effect of the free variables on the behavior of the reached plots to a few achieved solutions for the nonlinear rational exact cases was also explored depending upon the nature of nonlinearities. The dynamical properties of the obtained solutions are analyzed and shown by plotting some density, two and three-dimensional images. We believe that our results would pave a way for future research generating optical memories based on the nonparaxial solitons.