Explicit Traveling Wave Solutions and Their Dynamical Behaviors for the Coupled Higgs Field Equation (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we focus on the traveling wave solutions of the coupled Higgs field equation from the perspective of dynamical systems. Throughthe phase portraits, in addition to periodic wave solutions and solitary wavesolutions, we also obtain explicit periodic singular wave solutions, singularwave solutions and kink wave solutions, which were not found in the previousworks. The dynamical behavior of these solutions and their internal relationsare revealed through asymptotic analysis. The results will help supplementthe study of field equation.
Keywords: Coupled Higgs field equation; Traveling wave solutions; Kink wave solutions.