A dense focusing Ablowitz-Ladik soliton gas and its asymptotics
Mathematical Physics
2026-03-18 v1 Analysis of PDEs
math.MP
Abstract
In this paper, we propose a soliton gas solution for the focusing Ablowitz-Ladik system. This solution is defined as the large N limit of the N-soliton solution, and arises from a continuous spectrum of poles that accumulate within two disjoint intervals on the imaginary axis. We show that this gas solution admits a Fredholm determinant representation. By further exploring its Riemann-Hilbert characterization, we are able to establish the large-space asymptotics at t = 0 and large-time asymptotics of the gas solution.
Keywords
Cite
@article{arxiv.2603.16696,
title = {A dense focusing Ablowitz-Ladik soliton gas and its asymptotics},
author = {Meisen Chen and Engui Fan and Zhaoyu Wang and Yiling Yang and Lun Zhang},
journal= {arXiv preprint arXiv:2603.16696},
year = {2026}
}