Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 020, 23 pages      arXiv:1403.1012      https://doi.org/10.3842/SIGMA.2014.020
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa

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

Russell Johnson a and 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

Received October 17, 2013, in final form February 27, 2014; Published online March 05, 2014

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].

Key words: Sturm-Liouville problem; m-functions; zero-curvature equation; hierarchy of evolution equations; recursion system.

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