Nonparaxial pulse propagation in a planar waveguide with Kerr–like and quintic nonlinearities; computational simulations

This article investigates some novel solitary wave solutions of the cubic-quintic nonlinear Helmholtz equation by implementing two recent analytical (Khater II and generalized exponential methods) techniques. As a result of seeing the nonparaxial effect, this model was developed to show how a pulse propagates in a planar waveguide with Kerr-like and quintic nonlinearities as well as spatial dispersion. When the traditional approximation of a slowly changing envelope fails, this effect takes over. Some novel soliton wave solutions are obtained and formulated in distinct forms such as rational, hyperbolic, and trigonometric forms. The obtained solutions are represented through various figures’ types to show the physical and dynamical behavior of the nonparaxial pulse propagation. The model’s features are demonstrated, such as its intriguing bright, anti-bright, periodic, singular, gray, chirped anti-dark, and dark solitary waves depending upon the nature of nonlinearities. The solutions’ originality is discussed by comparing it with those constructed in recently published articles. All built results are checked their accuracy by putting them back into the original model by employing Mathematica 12.