It is known that a transform of Liouville type allows one to pass from an equation of the Korteweg-de Vries (K-dV) hierarchy to a corresponding equation of the Camassa-Holm (CH) hierarchy. We give a systematic development of the correspondence between these hierarchies by using the coefficients of asymptotic expansions of certain Green’s functions. We illustrate our procedure with some examples.
On the Camassa-Holm and K-dV hierarchies / R. Johnson; L. Zampogni. - In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. - ISSN 1040-7294. - STAMPA. - 22:(2010), pp. 331-366. [10.1007/s10884-010-9167-0]
On the Camassa-Holm and K-dV hierarchies
JOHNSON, RUSSELL ALLAN;
2010
Abstract
It is known that a transform of Liouville type allows one to pass from an equation of the Korteweg-de Vries (K-dV) hierarchy to a corresponding equation of the Camassa-Holm (CH) hierarchy. We give a systematic development of the correspondence between these hierarchies by using the coefficients of asymptotic expansions of certain Green’s functions. We illustrate our procedure with some examples.
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