R. Johnson, L. Zampogni
On the Camassa-Holm and K-dV Hierarchies
Preprint series: ESI preprints

MSC:

34C35 Dynamical systems, See also {54H20, 58Fxx, 70-XX}

54H20 Topological dynamics, See also {28Dxx, 34C35, 58Fxx}

58F99 None of the above but in this section

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.), See also {58F07}

34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)

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 \cite{BSS,MK}. 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.


Keywords: Liouville transformation, K-dV hierarchy, CH hierarchy, Green's function