Dynamical behavior of solitons in the Landau-Ginzburg-Higgs equation by using efficient techniques

This paper investigates the dynamics of the nonlinear Landau-Ginzburg-Higgs equation within the domain of superfluids and Bose-Einstein condensates. The primary focus is on exploring novel exact solutions within this equation. To obtain soliton solutions of the proposed nonlinear model, a modified Sardar sub-equation method and an extended modified tanh function method are employed. From a significant physical perspective, a diverse range of solutions is presented, encompassing bright solitons, dark solitons, singular solitons, combo dark-bright solitons, dark-singular solitons, periodic solutions, exponential solutions, and rational solutions. The study utilizes 2D and 3D visualizations of the computed wave solutions to effectively illustrate the internal structure of the phenomenon. This study also presents a comparative analysis of wave speed parameters using 2D graphs. By visualizing these parameters, the research highlights the variations and intricate behavior of the soliton solutions, further enhancing the understanding of the nonlinear Landau-Ginzburg-Higgs equation. The study marks the first application of the modified Sardar subequation method and the extended modified tanh function method to the nonlinear Landau-Ginzburg-Higgs equation. This combination provides a comprehensive model for capturing complicated biological and physical events, with increased predictive power and adaptability. © 2025 World Scientific Publishing Company.