Lamé Potentials and the Stationary (m)KdV Hierarchy

DOI10.1002/mana.19951760107zbMath0843.35100OpenAlexW1965764789MaRDI QIDQ4866711

Rudi Weikard, Friedrich Gesztesy

Publication date: 18 March 1996

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19951760107

zbMATH Keywords

elliptic finite-gap solutionselliptic Weierstrass functionKorteweg-de Vries and modified Korteweg-de Vries hierarchyLamé-Ince potentials

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) Theta functions and curves; Schottky problem (14H42)

Related Items (16)

Treibich-Verdier potentials and the stationary (m)KdV hierarchy ⋮ Picard potential and Hill's equation on a torus ⋮ On algebraic multiplicity of (anti)periodic eigenvalues of Hill’s equations ⋮ An explicit characterization of Calogero–Moser systems ⋮ Quasiperiodic and periodic solutions for vector nonlinear Schrödinger equations ⋮ Exact number and non-degeneracy of critical points of multiple Green functions on rectangular tori ⋮ On a theorem of Picard ⋮ Elliptic solitons with free constants and their isospectral deformations ⋮ Differential Resultant, Computer Algebra and Completely Integrable Dynamical Systems ⋮ Spectrum of the Lamé operator and application. I: Deformation along \(\operatorname{Re} \tau = \frac{ 1}{ 2} \) ⋮ On algebro-geometric simply-periodic solutions of the KdV hierarchy ⋮ A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy ⋮ Spectrum of the Lamé operator and application. II: When an endpoint is a cusp ⋮ Exact solutions for a class of integrable Hénon–Heiles-type systems ⋮ Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach ⋮ An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy

Cites Work

• Elliptic solutions of the Korteweg-de Vries equation
• Loop groups and equations of KdV type
• Theta functions and non-linear equations
• VII—Further Investigations into the Periodic Lamé Functions
• Unnamed Item

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