On the compatible weakly nonlocal Poisson brackets of hydrodynamic type.
Maltsev, Andrei Ya. (2002)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “The averaging of nonlocal Hamiltonian structures in Whitham's method.”
On the compatible weakly nonlocal Poisson brackets of hydrodynamic type.
Andrew Lenard: a mystery unraveled.
Praught, Jeffery, Smirnov, Roman G. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Modulation of the Camassa-Holm equation and reciprocal transformations
Simonetta Abenda, Tamara Grava (2005)
Annales de l’institut Fourier
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We derive the modulation equations (Whitham equations) for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit a 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...