We introduce a hierarchy of evolution equations based on the Sturm-Liouville equation -(pφ?) + qφ = λyφ. 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 / R. Johnson; L. Zampogni. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - STAMPA. - 11:(2011), pp. 555-591. [10.1515/ans-2011-0305]
The Sturm-Liouville hierarchy of evolution equations
JOHNSON, RUSSELL ALLAN;
2011
Abstract
We introduce a hierarchy of evolution equations based on the Sturm-Liouville equation -(pφ?) + qφ = λyφ. 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.
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