- 03-400 Bambusi D.
- Birkhoff normal form for some quasilinear Hamiltonian PDEs
Sep 3, 03
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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.