A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy

DOI10.1007/BF02392748zbMath0955.34073OpenAlexW1983029450MaRDI QIDQ1273530

Rudi Weikard, Friedrich Gesztesy

Publication date: 13 February 2001

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392748

zbMATH Keywords

AKNS hierarchyelliptic functionsnonlinear evolution equationsKdV hierarchyfirst-order differential operatorsPicard-AKNS potentials

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) KdV equations (Korteweg-de Vries equations) (35Q53) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items

The AKNS hierarchy and finite-gap Schrödinger potentials, Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators, Hierarchies and Hamiltonian structures of the nonlinear Schrödinger family using geometric and spectral techniques, On the spectrum of the periodic focusing Zakharov-Shabat operator, Elliptic finite-band potentials of a non-self-adjoint Dirac operator, A Schauder and Riesz basis criterion for non-self-adjoint Schrödinger operators with periodic and antiperiodic boundary conditions, An explicit characterization of Calogero–Moser systems, Quasiperiodic and periodic solutions for vector nonlinear Schrödinger equations, On a theorem of Picard, Quasi-periodic solutions of mixed AKNS equations, Algebro-geometric constructions of the Wadati-Konno-Ichikawa flows and applications, A criterion for Hill operators to be spectral operators of scalar type, Spectral analysis of Darboux transformations for the focusing NLS hierarchy, Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach, Elliptic solitons, Fuchsian equations, and algorithms, On a theorem of Halphen and its application to integrable systems

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