Publication: Integration of pair flows of the Camassa-Holm hierarchy
Integration of pair flows of the Camassa-Holm hierarchy
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Loubet, E. (2007). Integration of pair flows of the Camassa-Holm hierarchy. In M. Pinsky & B. Birnir (Eds.), Probability, geometry and integrable systems (No. 55; Vol. 55, pp. 261–285). Cambridge Univ. Press. http://www.msri.org/communications/books/Book55/files/12loubet.pdf
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We present the integration of the “pair” flows associated to the Camassa–Holm (CH) hierarchy i.e., an explicit exact formula for the update of the initial velocity profile in terms of initial data when run by the flow associated to a Hamiltonian which (up to a constant factor) is given by the sum of the reciprocals of the squares of any two eigenvalues of the underlying spectral problem. The method stems from the integration of “individual” flows of the CH hierarchy described in [Loubet 2006; McKean 2003], and is seen to be more gener
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Loubet, E. (2007). Integration of pair flows of the Camassa-Holm hierarchy. In M. Pinsky & B. Birnir (Eds.), Probability, geometry and integrable systems (No. 55; Vol. 55, pp. 261–285). Cambridge Univ. Press. http://www.msri.org/communications/books/Book55/files/12loubet.pdf
