Galerkin averaging method and Poincaré normal form for some quasilinear PDEs

Dario Bambusi

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Modulation of the Camassa-Holm equation and reciprocal transformations

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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...

A KAM-theorem for some nonlinear partial differential equations

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Antonio Giorgilli (1988)

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KAM theory for the hamiltonian derivative wave equation

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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.