Displaying similar documents to “On the mechanics with noncontinuous hamiltonians”

Geometric integrators for piecewise smooth Hamiltonian systems

Philippe Chartier, Erwan Faou (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we consider Hamiltonian systems. We prove the existence of a first derivative of the flow with respect to initial values and show that it satisfies the symplecticity condition almost everywhere in the phase-space. In a second step, we present a geometric integrator for such systems (called the method) based on B-splines interpolation and a splitting method introduced by McLachlan and Quispel [.  (2003) 411–418], and we prove it is convergent, and that...

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...

Galerkin averaging method and Poincaré normal form for some quasilinear PDEs

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...

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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