Consider a Hamiltonian PDE having an elliptic equilibrium at zero. Assuming a suitable condition on the frequencies we will construct a canonical transformation putting the system in Birkhoff normal form up to a small reminder. In the case of quasilinear systems the normal form will be used to describe the dynamics of smooth solutions of small amplitude. Applications to the water wave problem and to quasilinear wave equations will be given.
Birkhoff normal form for some quasilinear Hamiltonian PDEs / D. Bambusi - In: XIVth International Congress on Mathematical Physics / [a cura di] Jean-Claude Zambrini. - Hackensack, NJ : World Scientific, 2006. - ISBN 978-981-256-201-2. - pp. 273-280 (( Intervento presentato al 14. convegno International Congress on Mathematical Physics tenutosi a Lisbona, Portugal nel 2003 [10.1142/9789812704016_0024].
Birkhoff normal form for some quasilinear Hamiltonian PDEs.
D. BambusiPrimo
2006
Abstract
Consider a Hamiltonian PDE having an elliptic equilibrium at zero. Assuming a suitable condition on the frequencies we will construct a canonical transformation putting the system in Birkhoff normal form up to a small reminder. In the case of quasilinear systems the normal form will be used to describe the dynamics of smooth solutions of small amplitude. Applications to the water wave problem and to quasilinear wave equations will be given.
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