A new hierarchy of integrable system of dimensions: from Newton's law to generalized Hamiltonian system. II.
Huang, Xuncheng, Tu, Guizhang (2006)
International Journal of Mathematics and Mathematical Sciences
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Huang, Xuncheng, Tu, Guizhang (2006)
International Journal of Mathematics and Mathematical Sciences
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J. Golenia, O. Hentosh, A. Prykarpatsky (2007)
Open Mathematics
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The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.
Jurdjevic, V. (1999)
Annals of Mathematics. Second Series
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Praught, Jeffery, Smirnov, Roman G. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Maltsev, Andrei Ya. (2002)
International Journal of Mathematics and Mathematical Sciences
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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...
Charles-Michel Marle (2003)
Banach Center Publications
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Dragt, Alex J. (1997)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Chavchanidze, G. (2003)
Georgian Mathematical Journal
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Xu, Taixi, Mu, Weihua, Qiao, Zhijun (2006)
International Journal of Mathematics and Mathematical Sciences
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Udrişte, Constantin, Teleman, Ana-Maria (2004)
International Journal of Mathematics and Mathematical Sciences
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Xavier Gràcia, Josep M. Pons (1996)
Extracta Mathematicae
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