Moduli spaces for PT-regularized solitons

TL;DR

This paper constructs and analyzes moduli spaces for PT-regularized solitons in a 1+1 dimensional classical field theory, capturing soliton dynamics, scattering, and complex multi-soliton interactions.

Contribution

It introduces a novel moduli space framework for PT-regularized solitons, including multi-soliton scattering and triple bouncing phenomena.

Findings

One-dimensional moduli space effectively describes soliton center of mass motion.

Time-delay and spatial displacements are extractable from the moduli space.

Two-dimensional moduli space captures triple bouncing scattering among solitons.

Abstract

We construct and analyse the moduli space (collective coordinates) for a classical field theory in 1 + 1 dimensions that possesses complex stable multi-soliton solutions with real energies when PT-regularized. For the integrable Bullough-Dodd model we show, by comparing with the exact solutions, that a one-dimensional moduli space captures well the main feature of the centre of mass motion of the one and two-soliton solutions. We demonstrate that even the time-delay and spatial displacements occurring for the one-soliton constituents in a multi-soliton scattering process can be extracted from a moduli space analysis. We propose a two dimensional moduli space to describe the newly found triple bouncing scattering amongst the constituents of a dark two double peakon scattering.