We introduce a hierarchy of evolution equations based on the Sturm-Liouville equation. Our hierarchy includes the Korteweg-de Vries (K-dV) and the Camassa-Holm (CH) hierarchy. We determine a class of solutions of the hierarchy which are of algebro-geometric type. The initial condition of such a solution is drawn from a finite-gap isospectral class of the Sturm-Liouville equation.
The Sturm-Liouville hierarchy of evolution equations
ZAMPOGNI, Luca
2011
Abstract
We introduce a hierarchy of evolution equations based on the Sturm-Liouville equation. Our hierarchy includes the Korteweg-de Vries (K-dV) and the Camassa-Holm (CH) hierarchy. We determine a class of solutions of the hierarchy which are of algebro-geometric type. The initial condition of such a solution is drawn from a finite-gap isospectral class of the Sturm-Liouville equation.File in questo prodotto:
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