A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $\mathbb{R}$

Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Singularity in context of PDEs (35A21)

Related Items

Deformation of the spectrum for Darboux-Treibich-Verdier potential along $\mathrm{Re}\,\tau =\frac{1}{2}$

Cites Work

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Mean field equations, hyperelliptic curves and modular forms. I
On Darboux-Treibich-Verdier potentials
Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems
Exceptional coverings and sums of 4 triangular numbers
Picard potential and Hill's equation on a torus
The Heun equation and the Calogero-Moser-Sutherland system. I: The Bethe ansatz method
Treibich-Verdier potentials and the stationary (m)KdV hierarchy
On algebro-geometric simply-periodic solutions of the KdV hierarchy
The geometry of generalized Lamé equation. I
The geometry of generalized Lamé equation. II: Existence of pre-modular forms and application
On the spectra of real and complex Lamé operators
On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV poten\-tials
The Heun equation and the Calogero-Moser-Sutherland system. IV: The Hermite-Krichever ansatz
Sharp Nonexistence Results for Curvature Equations with Four Singular Sources on Rectangular Tori
The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations
Complex hill's equation and the complex periodic korteweg-de vries equations
The Heun Equation and the Calogero-Moser-Sutherland System III: The Finite-Gap Property and the Monodromy
An explicit characterization of Calogero–Moser systems
VII—Further Investigations into the Periodic Lamé Functions

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