arXiv subjects

Fritz Gesztesy

Publications and source records attributed to Fritz Gesztesy.

165 records · Page 10Linked to original sources

arXiv1997

A Characterization of All Elliptic Solutions of the AKNS Hierarchy

An explicit characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy is presented. Our approach is based on (an extension of) a classical theorem of Picard, which guarantees the existence of solutions which are elliptic of the second kind for n-th order ordinary differential equations with elliptic coefficients associated with a common period lattice. As by-products we offer a detailed Floquet analysis of Dirac-type differential expressions with periodic coefficients, specifically emphasizing algebro-geometric coefficients, and a constructive reduction of singular hyperelliptic curves and their Baker-Akhiezer functions to the nonsingular case.

solv-int↗

arXiv1993

Trace formulae and inverse spectral theory for Schrödinger operators

We extend the well-known trace formula for Hill's equation to general one-dimensional Schrödinger operators. The new function $ξ$, which we introduce, is used to study absolutely continuous spectrum and inverse problems.

math.SP↗

arXiv1992

New types of soliton solutions

We announce a detailed investigation of limits of N-soliton solutions of the Korteweg-deVries (KdV) equation as $N$ tends to infinity. Our main results provide new classes of KdV-solutions including in particular new types of soliton-like (reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one-dimensional Schrödinger operators and explicitly construct smooth and real-valued potentials that yield a purely absolutely continuous spectrum on the nonnegative real axis and give rise to an eigenvalue spectrum that includes any prescribed countable and bounded subset of the negative real axis.

math.AP↗