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

[摘要] 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].

[关键词] Sturm–Liouville problem;m-functions;zero-curvature equation;hierarchy of evolution equations;recursion system