A generalization for Peakon's solitary wave and Camassa-Holm equation.
Boldea, Costin-Radu (1997)
General Mathematics
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Boldea, Costin-Radu (1997)
General Mathematics
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Gupta, V.G., Sharma, P. (2010)
Acta Universitatis Apulensis. Mathematics - Informatics
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Giulio Mattei (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In questo lavoro si ricavano: 1) l’equazione d’onda linearizzata, 2) la formulazione Lagrangiana, 3) la formulazione Hamiltoniana, nella teoria della propagazione ondosa in un fluido incomprimibile descritto dalle equazioni della magnetofluidodinamica ideale in presenza di corrente Hall.
Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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Praught, Jeffery, Smirnov, Roman G. (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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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...
Zhang, Dongfeng, Cheng, Rong (2010)
Fixed Point Theory and Applications [electronic only]
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Yuan, Xiaoping (2003)
International Journal of Mathematics and Mathematical Sciences
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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...
Gary Chartrand, S. F. Kapoor (1974)
Colloquium Mathematicae
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Giulio Mattei (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In questo lavoro si ricavano: 1) l'equazione d'onda linearizzata, 2) la formulazione Lagrangiana, 3) la formulazione Hamiltoniana, nella teoria della propagazione ondosa in un fluido comprimibile descritto dalle equazioni della magnetofluidodinamica ideale in presenza di corrente Hall.
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.
Robert McLachlan (1993/94)
Numerische Mathematik
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