On the parametrization of finite-gap solutions by frequency and wavenumber vectors and a theorem of I. Krichever

DOI10.1007/BF00750304zbMath0774.35070MaRDI QIDQ2368138

Ramil' F. Bikbaev, Sergej B. Kuksin

Publication date: 7 November 1993

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

hyperelliptic Riemann surfaceparametrization for the Korteweg-de Vries equationproof of Krichever's theorem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (12)

Nondegeneracy of amplitude-frequency modulation for finite-gap solutions of integrable nonlinear equations ⋮ KdV Hamiltonian as a function of actions ⋮ Large KAM tori for quasi-linear perturbations of KdV ⋮ On the wellposedness of the KdV/KdV2 equations and their frequency maps ⋮ On the local coordinates on the manifold of finite-gap solutions of the KdV equation ⋮ Complex Whitham deformations in problems with ``integrable instability ⋮ Complex Whitham deformations in problems with ``integrable instability ⋮ Symplectic structures for the cubic Schrödinger equation in the periodic and scattering case ⋮ On the stability of periodic multi-solitons of the KdV equation ⋮ On the convexity of the KdV Hamiltonian ⋮ Nekhoroshev theorem for the periodic Toda lattice ⋮ Symmetries of the periodic Toda lattice, with an application to normal forms and perturbations of the lattice with Dirichlet boundary conditions

Cites Work

• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation

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