The algebraic-geometric AKNS potentials

DOI10.1017/S0143385700003783zbMath0636.35077OpenAlexW2002767943MaRDI QIDQ3775938

Corrado De Concini, Russell A. Johnson

Publication date: 1987

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700003783

zbMATH Keywords

Floquet exponentalgebraic-geometric potentialsrandom ergodic Schrödinger operatorsSchrödinger and AKNS operatorsWeyl m- functions

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Partial differential equations of mathematical physics and other areas of application (35Q99) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items (26)

On the nature of the spectrum of the quasi-periodic Schrödinger operator. ⋮ Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators ⋮ Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators ⋮ Some examples of generalized reflectionless Schrödinger potentials ⋮ The Ten Martini problem ⋮ m-functions and Floquet exponents for linear differential systems ⋮ On solutions of nonlinear Schrödinger equations with Cantor-type spectrum ⋮ On the Lyapunov exponent of certain \(SL (2,\mathbb R)\)-valued cocycles. II ⋮ Monotonic cocycles ⋮ Resonance tongues in the quasi-periodic Hill-Schrödinger equation with three frequencies ⋮ Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation ⋮ Rotation number and exponential dichotomy for linear Hamiltonian systems: from theoretical to numerical results ⋮ On \({SL(2, \mathbb R)}\) valued smooth proximal cocycles and cocycles with positive Lyapunov exponents over irrational rotation flows ⋮ A biography of Russell A. Johnson ⋮ Resonance tongues and spectral gaps in quasi-periodic Schrödinger operators with one or more frequencies. A numerical exploration ⋮ Cantor spectrum and KDS eigenstates ⋮ Essential closures and AC spectra for reflectionless CMV, Jacobi, and Schrödinger operators revisited ⋮ Equality of the spectral and dynamical definitions of reflection ⋮ On the Camassa-Holm and K-dV hierarchies ⋮ Combinatorial rigidity for unicritical polynomials ⋮ Remarks on Linear Differential Systems with Measurable Coefficients ⋮ Hopf bifurcation from nonperiodic solutions of differential equations. I: Linear theory ⋮ Golden mean renormalization for the almost Mathieu operator and related skew products ⋮ On the Kotani-Last and Schrödinger conjectures ⋮ Right limits and reflectionless measures for CMV matrices ⋮ An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Almost periodic Schrödinger operators. II: The integrated density of states
• On the even-order vanishing of Jacobian theta functions
• Spectral properties of disordered systems in the one-body approximation
• The rotation number for almost periodic potentials
• Existence of dichotomies and invariant splittings for linear differential systems. I
• E-compact extensions of topological spaces
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• The spectrum of Hill's equation
• A spectral theory for linear differential systems
• Exponential dichotomies and transversal homoclinic points
• Theta functions on Riemann surfaces
• Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension
• The Periodic Cubic Schrõdinger Equation
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• The Toda lattice. II. Existence of integrals
• SPECTRAL OPERATORS IN A DIRECT SUM OF HILBERT SPACES
• Isolated Invariant Sets for Flows on Vector Bundles
• A Characterization of the Spectra of One-Dimensional Wave Equations

This page was built for publication: The algebraic-geometric AKNS potentials