A new approach to separation of variables for the Clebsch integrable system. Part II: Inversion of the Abel--Prym map

Autor:	Fedorov, Yu., Magri, F., Skrypnyk, T.
Rok vydání:	2021
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematics - Algebraic Geometry 14H40 14H70 14K25 37J35 70H06
Druh dokumentu:	Working Paper
Popis:	This is the second part of a paper describing a new concept of separation of variables applied to the classical Clebsch integrable case. The quadratures obtained in Part I (also uploaded in arXiv.org) lead to a new type of the Abel map which contains Abelian integrals on two different algebraic curves. Here we interprete it as from the product of the two curves to the Prym variety of one of them, show that the map is well defined although not a bijection. We analyse its properties and formulate a new extention of the Riemann vanishing theorem, which allows to invert the map in terms of theta-functions of higher order. Lastly, we describe how to express the original variables of the Clebsch system in terms of the preimages of the map. This enables one to obtain theta-function solution whose structure is different from that found long time ago by F. K\"otter. Comment: The key points of this submission had been reported in the FDIS 2019 conference and some previous workshops
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.03599 Zobrazit plný text záznamu View this record from Arxiv