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Article Dans Une Revue Journal of Geometry and Physics Année : 2021

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

Résumé

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.
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hal-03234952 , version 1 (02-01-2023)

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Paternité - Pas d'utilisation commerciale

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Pierre Gaillard. 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, 2021, 161, pp.104059. ⟨10.1016/j.geomphys.2020.104059⟩. ⟨hal-03234952⟩
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