The Bullough-Dodd model coupled to matter fields

TL;DR

This paper explores integrable extensions of the Bullough-Dodd model, including matter fields and conformal invariance, constructing explicit soliton solutions and revealing a confinement mechanism within certain models.

Contribution

It introduces new integrable models coupling matter fields to the Bullough-Dodd framework, with explicit soliton solutions and analysis of their symmetry and confinement properties.

Findings

Explicit one and two-soliton solutions constructed

Identification of a confinement mechanism within a specific model

Extension to conformally invariant and matter-coupled theories

Abstract

The Bullough-Dodd model is an important two dimensional integrable field theory which finds applications in physics and geometry. We consider a conformally invariant extension of it, and study its integrability properties using a zero curvature condition based on the twisted Kac-Moody algebra A_2^{(2)}. The one and two-soliton solutions as well as the breathers are constructed explicitly . We also consider integrable extensions of the Bullough-Dodd model by the introduction of spinor (matter) fields. The resulting theories are conformally invariant and present local internal symmetries. All the one-soliton solutions, for two examples of those models, are constructed using an hybrid of the dressing and Hirota methods. One model is of particular interest because it presents a confinement mechanism for a given conserved charge inside the solitons.