The algebraic-geometric AKNS potentials
Authors:
- 1 March 1987
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 7 (1) , 1-24
Abstract
We characterize the algebraic-geometric potentials for the Schrödinger and AKNS operators using the Weyl m-functions and the Floquet exponent for these operators. The characterization is this: among random ergodic Schrödinger operators, the alebraic-geometric potentials are those for which (i) the spectrum is a union of finitely many intervals (or bands); (ii) the Lyapounov exponent vanishes on the spectrum.Keywords
This publication has 21 references indexed in Scilit:
- Almost periodic Schr dinger operatorsCommunications in Mathematical Physics, 1983
- The rotation number for almost periodic potentialsCommunications in Mathematical Physics, 1982
- The Periodic Cubic Schrõdinger EquationStudies in Applied Mathematics, 1981
- Spectral properties of disordered systems in the one-body approximationCommunications in Mathematical Physics, 1980
- The spectrum of Hill's equationInventiones Mathematicae, 1975
- Isolated Invariant Sets for Flows on Vector BundlesTransactions of the American Mathematical Society, 1975
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear ProblemsStudies in Applied Mathematics, 1974
- A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. IFunctional Analysis and Its Applications, 1974
- E-compact extensions of topological spacesFunctional Analysis and Its Applications, 1974
- ber gew hnliche Differentialgleichungen mit Singularit ten und die zugeh rigen Entwicklungen willk rlicher FunktionenMathematische Annalen, 1910