Dressing method for the vector sine-Gordon equation and its soliton interactions

TL;DR

This paper develops a dressing method to find exact multi-soliton solutions for the vector sine-Gordon equation, analyzing soliton interactions and shifts based on pole positions.

Contribution

It introduces a novel dressing method for the vector sine-Gordon equation and derives explicit formulas for soliton solutions and their interactions.

Findings

Explicit formulas for one kink and breather solutions.

Analysis of two-soliton interaction effects.

Position and phase shifts depend only on dressing matrix poles.

Abstract

In this paper, we develop the dressing method to study the exact solutions for the vector sine-Gordon equation. The explicit formulas for one kink and one breather are derived. The method can be used to construct multi-soliton solutions. Two soliton interactions are also studied. The formulas for position shift of the kink and position and phase shifts of the breather are given. These quantities only depend on the pole positions of the dressing matrices.