The averaging of nonlocal Hamiltonian structures in Whitham's method.
Maltsev, Andrei Ya. (2002)
International Journal of Mathematics and Mathematical Sciences
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Maltsev, Andrei Ya. (2002)
International Journal of Mathematics and Mathematical Sciences
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Guha, Partha (2004)
International Journal of Mathematics and Mathematical Sciences
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Praught, Jeffery, Smirnov, Roman G. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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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...
Nutku, Yavuz (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Sergyeyev, Artur (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Chiara Esposito (2015)
Banach Center Publications
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In this paper we recall the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group theories.
Huang, Xuncheng, Tu, Guizhang (2006)
International Journal of Mathematics and Mathematical Sciences
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