New waves solutions of a nonlinear Landau–Ginzburg–Higgs equation: The Sardar-subequation and energy balance approaches

This article investigates the significance of the unsteady nonlinear Landau-Ginzburg-Higgs equation in the context of superfluids and Bose–Einstein condensates. The problem of interest is the search for traveling wave solutions within this equation. To tackle this problem, the Sardar-sub equation and energy balance approaches are employed. Through these methods, a variety of traveling wave solutions are obtained, expressed in terms of cosine functions, generalized hyperbolic functions, and generalized trigonometric functions. The obtained solutions encompass different types of solitons, including bright and dark solitary waves, singular periodic wave, and hybrid wave solutions. The solutions are then visualized through 2D and 3D simulations. The findings of this study contribute to the understanding of the Landau-Ginzburg-Higgs equation and its application to superfluids and Bose–Einstein condensates. The novelty of this work lies in the utilization of the Sardar-sub equation and energy balance approaches to obtain diverse traveling wave solutions, surpassing previous efforts in the literature.