MATHEMATICAL ANALYSIS AND STUDY OF THE NUMEROUS TRAVELING WAVE BEHAVIOR FOR DIFFERENT WAVE VELOCITIES OF THE SOLITON SOLUTIONS FOR THE NONLINEAR LANDAU-GINSBERG-HIGGS MODEL IN NONLINEAR MEDIA

In this study, the nonlinear Landau-Ginsberg-Higgs (LGH) model is proposed and examined. The stated model is applied to analyze superconductivity and drift cyclotron waves in radially inhomogeneous plasma for coherent ion-cyclotron waves. This is undeniably a robust mathematical model in real-world applications. The generalized exponential rational function method (GERFM) is utilized to extract the suitable, useful, and further general solitary wave solutions of the LGH model via the traveling wave transformation. Furthermore, we investigate the effects of wave velocity in a particular time limit through a graphical representation of the examined solutions of the model to understand the dynamic behavior of the system. The attained results confirm the effectiveness and reliability of the considered scheme