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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Praught, Jeffery, Smirnov, Roman G. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Boldea, Costin-Radu (1997)
General Mathematics
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Massimiliano Berti, Luca Biasco, Michela Procesi (2013)
Annales scientifiques de l'École Normale Supérieure
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We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.
Chavchanidze, G. (2003)
Georgian Mathematical Journal
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Popowicz, Ziemowit (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Nutku, Yavuz (2007)
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...
Choudhuri, Amitava, Talukdar, B., Das, U. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Huang, Xuncheng, Tu, Guizhang (2006)
International Journal of Mathematics and Mathematical Sciences
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Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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Dario Bambusi (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We use the Galerkin averaging method to construct a coordinate transformation putting a nonlinear PDE in Poincaré normal form up to finite order. We also give a rigorous estimate of the remainder showing that it is small as a differential operator of very high order. The abstract theorem is then applied to a quasilinear wave equation, to the water wave problem and to a nonlinear heat equation. The normal form is then used to construct approximate solutions whose difference from true...
Henryk Żołądek (2011)
Banach Center Publications
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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.