The Sturm-Liouville Hierarchy of Evolution Equations and Limits of Algebro-Geometric Initial Data - Johnson, R.; Zampogni, L. (Symmetry, Integrability and Geometry: Methods and Applications, 2014)
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].