Inverse reconstruction of dissipative Kerr soliton interactions
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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BibTeX
@misc{silvestri2026inverse,
title = {{Inverse reconstruction of dissipative Kerr soliton interactions}},
author = {Carlo Silvestri and Panayotis G. Kevrekidis and Stephane Coen and C. Martijn de Sterke and Antoine F. J. Runge},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12269},
eprint = {2609.12269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12269},
}
RIS
TY - UNPB
TI - Inverse reconstruction of dissipative Kerr soliton interactions
AU - Carlo Silvestri
AU - Panayotis G. Kevrekidis
AU - Stephane Coen
AU - C. Martijn de Sterke
AU - Antoine F. J. Runge
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12269
UR - https://arxiv.org/abs/2609.12269
AB - 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.
ER -