Analysing the Landau-Ginzburg-Higgs equation in the light of superconductivity and drift cyclotron waves: Bifurcation, chaos and solitons

The Landau-Ginzburg-Higgs (LGH) equation is a fundamental framework for examining physical systems in the fields of condensed matter physics and field theory. This study delves into the LGH equation, particularly in the context of its relevance to superconductivity and drift cyclotron waves. Researchers have extensively investigated the LGH equation to uncover a diverse array of exact solutions, employing various methodologies. This manuscript centers on the examination of its dynamic properties, encompassing the analysis of phenomena such as bifurcations, sensitivity, chaotic behavior, and the emergence of soliton solutions. To achieve this, we employ the principles of planar dynamical theory, shedding light on the intricate behaviors embedded within the LGH equation. Furthermore, we utilize the tools and techniques provided by planar dynamical theory to derive soliton solutions for the LGH equation.