# Hill's operators with the potentials analytically dependent on energy

@article{Badanin2020HillsOW,
title={Hill's operators with the potentials analytically dependent on energy},
author={Andrey Badanin and Evgeny L. Korotyaev},
journal={arXiv: Mathematical Physics},
year={2020}
}
• Published 2 June 2020
• Mathematics
• arXiv: Mathematical Physics

## References

SHOWING 1-10 OF 24 REFERENCES
Third-order operators with three-point conditions associated with Boussinesq's equation
• Mathematics
Applicable Analysis
• 2019
We consider a non-self-adjoint third-order operator on the interval with real 1-periodic coefficients and three-point Dirichlet conditions at the points 0, 1 and 2. The eigenvalues of this operator
Wave equations with energy-dependent potentials
• Physics
• 2004
We study wave equations with energy-dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A
Third order operator with periodic coefficients on the real line
• Mathematics
• 2011
We consider the third order operator with periodic coefficients on the real line. This operator is used in the integration of the non-linear evolution Boussinesq equation. For the minimal smoothness
Even order periodic operators on the real line
• Mathematics
• 2010
We consider $2p\ge 4$ order differential operator on the real line with a periodic coefficients. The spectrum of this operator is absolutely continuous and is a union of spectral bands separated by
The periodic Euler-Bernoulli equation
We continue the study of the Floquet (spectral) theory of the beam equation, namely the fourth-order eigenvalue problem [a(x)u(x)] = λρ(x)u(x), -∞ < x < ∞, where the functions a and p are periodic
Schrödinger spectral problems with energy–dependent potentials as sources of nonlinear Hamiltonian evolution equations
We develop a method to derive infinite families of completely integrable nonlinear Hamiltonian evolution equations associated with Schrodinger spectral problems whose potential functions depend on
Some Applications of Operator-Valued Herglotz Functions
• Mathematics
• 2001
We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric
The spectral theory of the vibrating periodic beam
AbstractWe study the spectral theory of the fourth-order eigenvalue problem $$\left[ {a(x)u''(x)} \right]^{\prime \prime } = \lambda \rho (x)u(x), - \infty< x< \infty ,$$ , where the functionsa and ϱ
The Inverse Problem for the One-Dimensional Schrodinger Equation with an Energy-Dependent Potential. 2.
• Mathematics
• 1975
The one-dimensional Schrodinger equation is considered when the potential V+(k, x) depends on the energy k2 in the following way : V+(k, x) = U(x) + 2kQ(x) ; (U(x), Q(x)) belongs to a large class 1/