Degenerate Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation and the degenerate rational case

JOURNAL OF GEOMETRY AND PHYSICS

卷:161

Article

Gaillard, Pierre¹ 

[1] Univ Bourgogne Franche Comte, Inst Math Bourgogne, UMR 5584 CNRS, F-2100 Dijon, France

关键词: Riemann surface;    Riemann theta functions;    KdV equation;    Fredholm determinant;    Wronskians;   

DOI  :  10.1016/j.geomphys.2020.104059

来源: Elsevier

【 摘 要 】

We degenerate the finite gap solutions of the KdV equation from the general formulation given in terms of abelian functions when the gaps tend to points, to get solutions to the KdV equation given in terms of Fredholm determinants and wronskians. For this we establish a link between Riemann theta functions, Fredholm determinants and wronskians. This gives the bridge between the algebro-geometric approach and the Darboux dressing method. We construct also multi-parametric degenerate rational solutions of this equation. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free