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 (Beals et al., Adv Math 154, 2000; McKean, Commun Pure Appl Math 56 (7), 2003). 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
ZAMPOGNI, Luca
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 (Beals et al., Adv Math 154, 2000; McKean, Commun Pure Appl Math 56 (7), 2003). 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.File in questo prodotto:
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