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 -(p phi')' + q phi = lambda y phi, which is determined by data related to a Riemann surface of "infinite genus".
The Sturm-Liouville hierarchy of evolution equations II / R. Johnson; L. Zampogni. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - STAMPA. - 12:(2012), pp. 501-532. [10.1515/ans-2012-0305]
The Sturm-Liouville hierarchy of evolution equations II
JOHNSON, RUSSELL ALLAN;
2012
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 -(p phi')' + q phi = lambda y phi, which is determined by data related to a Riemann surface of "infinite genus".
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