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Geometry of KdV. IV: Abel sums, Jacobi variety, and theta function in the scattering case. (English) Zbl 0714.35074

[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).]
Reviewer: N.L.Maria

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
14K25 Theta functions and abelian varieties
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References:

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