Moduli spaces for PT-regularized 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.

19 pages, 5 figures

References in corpus (6)

• Collective Coordinates in One-Dimensional Soliton Models Revisited
• Resonance structures in kink-antikink collisions in a deformed sine-Gordon model
• From real fields to complex Calogero particles
• The Bullough-Dodd model coupled to matter fields
• Linearly stable and unstable complex soliton solutions with real energies in the Bullough-Dodd model
• Boundary metrics on soliton moduli spaces