An Explicit Solution of the Inverse Periodic Problem for Hill’s Equation

DOI10.1137/0518003zbMath0622.34021OpenAlexW2015913807MaRDI QIDQ3759172

Allan Finkel, Eli L. Isaacson, Eugene Trubowitz

Publication date: 1987

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0518003

zbMATH Keywords

inverse problemspectrumHill's operatorisospectral manifold

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Ordinary differential operators (34L99)

Related Items (15)

Treibich-Verdier potentials and the stationary (m)KdV hierarchy ⋮ Inverse problem for Sturm-Liouville and Hill equations ⋮ Spectral deformations of one-dimensional Schrödinger operators ⋮ On the symplectic structure of the phase space for periodic KdV, Toda, and defocusing NLS ⋮ Renormalized oscillation theory for Hamiltonian systems ⋮ A spectral transform for the matrix Hill's equation ⋮ Perturbations of orthogonal polynomials with periodic recursion coefficients ⋮ The periodic Euler-Bernoulli equation ⋮ A note on analyticity and Floquet isospectrality ⋮ The inverse periodic problem for Hill's equation with a finite-gap potential ⋮ Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach ⋮ A partial inverse Sturm--Liouville problem: Matching a step function potential to a finite eigenvalue list ⋮ Compactness of Floquet isospectral sets for the matrix Hill's equation ⋮ Fibration of the phase space for the Korteweg-de Vries equation ⋮ Explicit isospectral flows associated to the <scp>AKNS</scp> operator on the unit interval. II

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