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Elliptic Baker-Akhiezer Functions and an Application to an Integrable Dynamical System

J. Eilbeck
V. Enol'skii
Journal / Anthology

Journal of Mathematical Physics
Year: 1994
Volume: 35
Issue: 3
Page range: 1192-1201

An ansatz for elliptic Baker-Akhiezer functions is used to find new solutions for various spectral problems--the Sturm-Liouville problem with four and five-gap Lamé potentials and two third-order problems. One of the third-order problems is the classical Halphen equation with a spectral parameter. The eigenfunctions are used to construct elliptic solutions for integrable cases of a generalized Hénon-Heiles system.

*Mathematics > Calculus and Analysis > Differential Equations
*Mathematics > Calculus and Analysis > Special Functions