Geometry of KdV. IV: Abel sums, Jacobi variety, and theta function in the scattering case
type: Item
instance of: scholarly article
title: Geometry of KdV. IV: Abel sums, Jacobi variety, and theta function in the scattering case
zbMATH Open document ID: 0714.35074
DOI: 10.1007/BF01234429
published in: Inventiones Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143768
review text: [For part II see the second author, J. Stat. Phys. 46, No.5-6, 1115-1143 (1987; Zbl 0689.35076); part III is to appear.] The authors study the geometry of Korteweg-de Vries equations with Abel sums, Jacobi variety, and theta function in the scattering case. They identify the ``curve'', ``theta function'', and ``theta divisor'', and confirm that they share much of the familiar beautiful geometry. A cursory view of the full phase geometry is presented. But the principal object of study is a single invariant manifold and its complexification. [For part V see the second author, Commun. Pure Appl. Math. 42, No.5, 687-701 (1989; Zbl 0699.58062).]
reviewed by: N.L.Maria
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 14K25
zbMATH DE Number: 4175590
zbMATH Keywords: Korteweg-de Vries equations
zbMATH Keywords: theta function
zbMATH Keywords: invariant manifold
author: Nicholas M. Ercolani
author: Henry P. McKean
MaRDI profile type: Publication
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OpenAlex ID: W1984778623
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description: scientific article; zbMATH DE number 4175590