  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.
