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

In this paper, we study the coupled Higgs equation and its multi-component gener-alization 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.(c) 2023 Elsevier B.V. All rights reserved.