Modulation of Camassa--Holm equation and reciprocal transformations

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dc.creatorAbenda, Simonetta
dc.creatorGrava, Tamara
dc.date2005-06-15
dc.date2005-11-03
dc.date.accessioned2026-07-07T06:42:16Z
dc.date.available2026-07-07T06:42:16Z
dc.descriptionWe derive the modulation equations or Whitham equations for the Camassa--Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry of the bi-Hamiltonian structure of the KdV and CH modulation equations is quite different: indeed the KdV averaged bi-Hamiltonian structure can always be related to a semisimple Frobenius manifold while the CH one cannot.
dc.identifierhttps://arxiv.org/abs/math-ph/0506042
dc.identifierhttp://arxiv.org/abs/math-ph/0506042
dc.identifierAnnales de L' Institut Fourier vol. 55, 2005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101976
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleModulation of Camassa--Holm equation and reciprocal transformations
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