<p>The Landau–Ginzburg–Higgs equation, which arises within the framework of superfluids and Bose–Einstein condensates, is currently under investigation. The main objectives of this study are to obtain novel exact solutions using two analytical techniques and to analyze the corresponding phase portraits. The derived solutions include kink, anti-kink, dark, bright, singular, periodic singular, and complexion soliton solutions. Moreover, the complexion solutions incorporate various types of solitons, such as kink, anti-kink, bright, and dark solitons. The phase portraits of the studied equation are presented to illustrate the system’s dynamical behavior. Furthermore, a perturbation term is introduced into the system to investigate periodic, quasi-periodic, and chaotic motions via Poincaré sections. The stability of the obtained soliton solutions is also examined to ensure their physical relevance. In addition, two-dimensional and three-dimensional simulations are performed to visualize the solutions of the Landau–Ginzburg–Higgs equation, thereby enhancing the understanding of their dynamical and physical characteristics.</p>