Data di Pubblicazione:
2002
Citazione:
The nonlinear Schrödinger equation as a resonant normal form / D. Bambusi, A. Carati, A. Ponno. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - 2:1(2002), pp. 109-128.
Abstract:
Averaging theory is used to study the dynamics of dispersive equations taking the nonlinear Klein Gordon equation on the line as a model problem. For approximatively monochromatic initial data of amplitude $\epsilon$, we show that the corresponding solution consists of two non interacting wave packets, each one being described by a nonlinear Schr\"odinger equation. Such solutions are also proved to be stable over times of order $1/\epsilon^2$. We think that this approach puts into a new light the problem of obtaining modulations equations for general dispersive equations. The proof of our results requires a new use of normal forms as a tool for constructing approximate solutions.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Nonlinear Schr¨odinger equation; general dispersive equations.
Elenco autori:
D. Bambusi, A. Carati, A. Ponno
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