Study on dynamic features and traveling wave solutions of perturbed nonlinear Biswas–Milovic equation combining Kudryashov's law of refractive index

Abstract

This article mainly explores the Biswas–Milovic equation containing Kudryashov's refractive index law and nonlinear perturbation terms. We take the complete discrimination system for polynomial method and the trial equation method to implement qualitative and quantitative studies for the equation. We verify that the Hamiltonian of the dynamic system is conserved and apply the complete discrimination system of polynomial method to give the associated global phase diagrams, which are qualitatively analyzed to illustrate the presence of periodic solutions and solitons. In addition, we gain a classification of all single traveling wave solutions, provide optical wave patterns with specific parameters and validate the above findings.