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.
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Correa, F., Fring, A. & Taira, T. Moduli spaces for PT-regularized solitons. J. High Energ. Phys. 2022, 109 (2022). https://doi.org/10.1007/JHEP10(2022)109
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DOI: https://doi.org/10.1007/JHEP10(2022)109