Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators
Abstract
Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of 103 to 105 while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.
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BibTeX
@misc{akter2026fast,
title = {{Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators}},
author = {Sanzida Akter and Pradyoth Shandilya and Logan Courtright and Amir Leshem and Giuseppe D'Aguanno and Omri Gat and Curtis R. Menyuk},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10389},
eprint = {2609.10389},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10389},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators
AU - Sanzida Akter
AU - Pradyoth Shandilya
AU - Logan Courtright
AU - Amir Leshem
AU - Giuseppe D'Aguanno
AU - Omri Gat
AU - Curtis R. Menyuk
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10389
UR - https://arxiv.org/abs/2609.10389
AB - Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of 10^3 to 10^5 while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.
ER -