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

TL;DR

This paper investigates soliton solutions of the coupled Higgs equation and its multi-component extension, deriving explicit solutions using Hirota's method and Pfaffian techniques, and analyzing their interactions.

Contribution

It introduces a Pfaffian-based method to derive multi-soliton solutions for the coupled Higgs equations and explores their interaction properties.

Findings

Explicit one- and two-soliton solutions derived

Pfaffian identities established for the N-component system

Interaction behaviors such as elastic and inelastic collisions analyzed

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.