Quadratic operator pencils associated with the conservative Camassa-Holm flow

Abstract

We discuss direct and inverse spectral theory for a Sturm-Liouville type problem with a quadratic dependence on the eigenvalue parameter, which arises as the isospectral problem for the conservative Camassa-Holm flow.

38 pages

References in corpus (3)

• Long-Time Asymptotics for the Camassa-Holm Equation
• An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation
• On the isospectral problem of the dispersionless Camassa-Holm equation

Cited by in corpus (14)

• The inverse spectral problem for indefinite strings
• Spectral asymptotics for canonical systems
• Trace formulas and continuous dependence of spectra for the periodic conservative Camassa-Holm flow
• The Classical Moment Problem and Generalized Indefinite Strings
• The inverse spectral problem for periodic conservative multi-peakon solutions of the Camassa-Holm equation
• On the absolutely continuous spectrum of generalized indefinite strings
• Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy
• The Camassa--Holm Equation and The String Density Problem
• On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators
• Unique solvability of a coupling problem for entire functions
• Trace formulas and inverse spectral theory for generalized indefinite strings
• On the absolutely continuous spectrum of generalized indefinite strings II
• Generalized indefinite strings with purely discrete spectrum
• The conservative Camassa-Holm flow with step-like irregular initial data