The Sturm-Liouville Hierarchy of Evolution Equations II
Copyright policy )The Sturm-Liouville Hierarchy of Evolution Equations II
Abstract In a previous paper [15] we introduced the Sturm-Liouville (SL) hierarchy of evolution equations. This hierarchy includes the Korteveg-de Vries (K-dV) and the Camassa-Holm (CH) hierarchies. We also defined and discussed in detail the algebro-geometric solutions of the SL-hierarchy. In this paper, we broaden the class of algebro-geometric solutions in a substantial way. Namely, we define and discuss solutions of the SL-hierarchy lying in an isospectral class of the Sturm-Liouville problem −(pφ′)′ + qφ = λyφ, which is determined by data related to a Riemann surface of “infinite genus”.
- University of Perugia Italy
- University of Florence Italy
zero-curvature equation, Inverse problems involving ordinary differential equations, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Topological dynamics of nonautonomous systems, Sturm-Liouville problem; m-functions; zero-curvature equation; hierarchy of evolution equations; recursion system, m-functions, Sturm-Liouville problem, Sturm-Liouville theory, Sturm-Liouville problem, m-functions, zero-curvature equation, hierachy of evolution equations, recursion system, KdV equations (Korteweg-de Vries equations), hierarchy of evolution equations, recursion system
zero-curvature equation, Inverse problems involving ordinary differential equations, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Topological dynamics of nonautonomous systems, Sturm-Liouville problem; m-functions; zero-curvature equation; hierarchy of evolution equations; recursion system, m-functions, Sturm-Liouville problem, Sturm-Liouville theory, Sturm-Liouville problem, m-functions, zero-curvature equation, hierachy of evolution equations, recursion system, KdV equations (Korteweg-de Vries equations), hierarchy of evolution equations, recursion system
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