Russell Johnson, Luca Zampogni, “The Sturm–Liouville Hierarchy of Evolution Equations and Limits of Algebro-Geometric Initial Data”, SIGMA, 2014, Volume 10,020, 23 pp.

This article is cited in 2 papers

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

Russell Johnson^a, Luca Zampogni^b

^a Dipartimento di Sistemi e Informatica, Università di Firenze, Italy
^b Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Italy

Abstract: 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].

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

MSC: 37B55; 35Q53; 34A55; 34B24

Received: October 17, 2013; in final form February 27, 2014; Published online March 5, 2014

Language: English

DOI: 10.3842/SIGMA.2014.020