PreprintarXiv licencearXiv
A Jost--Pais theorem for the intermediate long wave equation
Abstract
For a one-dimensional Schrödinger operator, the transmission coefficient can be expressed as a Fredholm determinant. This fundamental discovery of Jost and Pais has recently proven very influential in the study of conserved quantities for the Korteweg--de Vries equation, whose Lax operator takes this form. In this paper, we obtain an analogue of this result for the intermediate long wave equation, where, startlingly, the transmission coefficient is given by a \emph{ratio} of Fredholm determinants. We then recover the original Jost--Pais result in the shallow-water limit and its analogue for the Benjamin--Ono equation as the infinite-depth limit.
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BibTeX
@misc{killip2026jostpais,
title = {{A Jost--Pais theorem for the intermediate long wave equation}},
author = {Rowan Killip and Monica Vişan and Yilun Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24966},
eprint = {2610.24966},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24966},
}
RIS
TY - UNPB
TI - A Jost--Pais theorem for the intermediate long wave equation
AU - Rowan Killip
AU - Monica Vişan
AU - Yilun Wu
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.24966
UR - https://arxiv.org/abs/2610.24966
AB - For a one-dimensional Schrödinger operator, the transmission coefficient can be expressed as a Fredholm determinant. This fundamental discovery of Jost and Pais has recently proven very influential in the study of conserved quantities for the Korteweg--de Vries equation, whose Lax operator takes this form. In this paper, we obtain an analogue of this result for the intermediate long wave equation, where, startlingly, the transmission coefficient is given by a \emph{ratio} of Fredholm determinants. We then recover the original Jost--Pais result in the shallow-water limit and its analogue for the Benjamin--Ono equation as the infinite-depth limit.
ER -