Search for items in this repository.
Geometric Integrability of the Camassa-Holm Equation. II
Hernández Heredero, Rafael and Reyes, Enrique G.
Geometric Integrability of the Camassa-Holm Equation. II.
"International Mathematics Research Notices"
It is known that the Camassa–Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equation admits nonlocal symmetries of “pseudo-potential type”: the standard quadratic pseudo-potential associated with the geodesics of the pseudo-spherical surfaces determined by (generic) solutions to CH, allows us to construct a covering π of the equation manifold of CH on which nonlocal symmetries can be explicitly calculated. In this article, we present the Lie algebra of (first-order) nonlocal π-symmetries for the CH equation, and we show that this algebra contains a semidirect sum of the loop algebra over sl(2,R) and the centerless Virasoro algebra. As applications, we compute explicit solutions, we construct a Darboux transformation for the CH equation, and we recover its recursion operator. We also extend our results to the associated Camassa–Holm equation introduced by J. Schiff.
Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
Check whether the spanish journal in which you have published an article allows you to also publish it under open access.