Integrable Systems in the Infinite Genus Limit
solv-int
2007-05-23 v1 可精确求解与可积系统
摘要
We provide an elementary approach to integrable systems associated with hyperelliptic curves of infinite genus. In particular, we explore the extent to which the classical Burchnall-Chaundy theory generalizes in the infinite genus limit, and systematically study the effect of Darboux transformations for the KdV hierarchy on such infinite genus curves. Our approach applies to complex-valued periodic solutions of the KdV hierarchy and naturally identifies the Riemann surface familiar from standard Floquet theoretic considerations with a limit of Burchnall-Chaundy curves.
引用
@article{arxiv.solv-int/9907009,
title = {Integrable Systems in the Infinite Genus Limit},
author = {Fritz Gesztesy},
journal= {arXiv preprint arXiv:solv-int/9907009},
year = {2007}
}
备注
LaTeX, 24 pages