Exact traveling wave solutions and conformable residual power series analysis of the fractional dual-mode nonlinear Landau–Ginzburg–Higgs model

This research examines solitary waves in a dual-mode nonlinear Landau–Ginzburg–Higgs setup utilizing novel treatments within a theoretical and numerical context. Following Korsunsky's approach, transformations are made to the nonlinear Landau–Ginzburg–Higgs equation of the dual-mode type. This formulation presents a framework in which wave propagation is modelled as dual wavefronts moving in opposite directions simultaneously. While dual-mode approaches have been implemented in the literature in various contexts, the combination of these methodologies along with the fractional order Landau–Ginzburg–Higgs formulations remains to be uncovered. For this work, analytical solutions are drawn using the generalized logistic equation approach. The solutions are shown to exhibit static and moving behaviour, tanh and anti-tanh wavefronts, as well as the coth-based wavefronts. The numerical and analytical solutions are shown to have high convergence and close agreement with each other. Various types of graphs, both 2D and 3D, are employed to depict multicriteria comparisons of the numerous solution characteristics.