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arXiv · 2609.12269

Inverse reconstruction of dissipative Kerr soliton interactions

Carlo Silvestri·Panayotis G. Kevrekidis·Stephane Coen·C. Martijn de Sterke·Antoine F. J. Runge
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Abstract

We reconstruct the pairwise interaction potential between dissipative Kerr solitons from the linear stability spectrum of a perfect soliton crystal solution of the Lugiato--Lefever equation. The solitons form an overdamped lattice whose positional eigenvalues encode the pairwise-force derivative, mirroring the extraction of microscopic interactions from phonon or relaxation spectra in condensed-matter systems. The method extends beyond quadratic dispersion and assumes no functional form for the interaction. Our theory predicts a novel state -the soft soliton crystal- which has vanishing stiffness and a diverging positional relaxation time, and also explains experimentally observed soliton steps as arising from a sign reversal of the pairwise-force derivative.

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Carlo Silvestri, Panayotis G. Kevrekidis, Stephane Coen, C. Martijn de Sterke, Antoine F. J. Runge. 2026-09-10. Inverse reconstruction of dissipative Kerr soliton interactions. https://arxiv.org/abs/2609.12269

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