The Sturm–Liouville Hierarchy of Evolution Equations and Limits of Algebro-Geometric Initial Data

Russell Johnson ; Luca Zampogni

Symmetry, integrability and geometry: methods and applications, Tome 10 (2014)

Résumé

The Sturm–Liouville hierarchy of evolution equations was introduced in [Adv. Nonlinear Stud. 11 (2011), 555–591] and includes the Korteweg-de Vries and the Camassa–Holm hierarchies. We discuss some solutions of this hierarchy which are obtained as limits of algebro-geometric solutions. The initial data of our solutions are (generalized) reflectionless Sturm–Liouville potentials [Stoch. Dyn. 8 (2008), 413–449].

Détail

Keywords: Sturm–Liouville problem; $m$-functions; zero-curvature equation; hierarchy of evolution equations; recursion system.

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