Geometry of KdV. IV: Abel sums, Jacobi variety, and theta function in the scattering case

DOI10.1007/BF01234429zbMath0714.35074OpenAlexW1984778623MaRDI QIDQ750771

H. P. jun. McKean, Nicholas M. Ercolani

Publication date: 1990

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143768

zbMATH Keywords

theta functioninvariant manifoldKorteweg-de Vries equations

Mathematics Subject Classification ID

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

Related Items (12)

Addition for the acoustic equation ⋮ The geometry of peaked solitons and billiard solutions of a class of integrable PDE's ⋮ The non-commutative Korteweg-de Vries hierarchy and combinatorial Pöppe algebra ⋮ The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles ⋮ Some connections between inverse scattering and solution hierarchies ⋮ Linear systems, Hankel products and the sinh-Gordon equation ⋮ Tau functions associated with linear systems ⋮ On soliton-type solutions of equations associated with N-component systems ⋮ On determinant expansions for Hankel operators ⋮ On geometric phases for soliton equations ⋮ Soliton Theory and Hankel Operators ⋮ Grassmannian flows and applications to non-commutative non-local and local integrable systems

Cites Work

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• Geometry of KdV. II: Three examples
• Geometry of KdV. I: Addition and the unimodular spectral classes
• Degenerate elliptic curves and resolution of uni- and bimodal singularities
• The spectrum of Hill's equation
• Fredholm determinants and inverse scattering problems
• Scattering theory for the Korteweg-de Vries (KdV) equation and its Hamiltonian interpretation
• Theta functions on Riemann surfaces
• On the geometry of a theorem of Riemann
• Method for Solving the Korteweg-deVries Equation
• Complex hill's equation and the complex periodic korteweg-de vries equations
• The infinite period limit of the inverse formalism for periodic potentials
• Hill’s surfaces and their theta functions
• Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem

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