Soliton dynamics to the Higgs equation and its multi-component generalization

Abstract

In this paper, we study the coupled Higgs equation and its multi-component generalization based on the Hirota’s direct method. One and two-soliton solutions of the coupled Higgs equation are derived by the perturbation approach. We express the N-soliton solutions in the form of Pfaffians and demonstrate that the N-component coupled Higgs equation turns out to be the Pfaffian identity. One and two-soliton solutions of the multi-component coupled Higgs equation are obtained from the Pfaffians. Starting from the explicit solutions, parallel solitons, periodic and nearly periodic interactions, elastic and inelastic collisions are investigated.