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arXiv · 2208.03199

Moduli spaces for PT-regularized solitons

Francisco Correa·Andreas Fring·Takanobu Taira
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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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Francisco Correa, Andreas Fring, Takanobu Taira. 2022-08-05. Moduli spaces for PT-regularized solitons. https://doi.org/10.1007/jhep10(2022)109

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