We discuss normal forms of the completely resonant nonlinear beam equation and nonlinear Schr?dinger equation. We work in n > 1 spatial dimensions and study both periodic and Dirichlet boundary conditions on cubes. We discuss the applications to the problem of finding quasi-periodic solutions. In the case of periodic boundary and the dimension n = 2, we apply KAM theory and prove the existence and stability of quasi-periodic solutions.

Procesi, M. (2010). A normal form for beam and non-local nonlinear Schrodinger equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 43, 1-13 [10.1088/1751-8113/43/43/434028].

A normal form for beam and non-local nonlinear Schrodinger equations

PROCESI, MICHELA
2010-01-01

Abstract

We discuss normal forms of the completely resonant nonlinear beam equation and nonlinear Schr?dinger equation. We work in n > 1 spatial dimensions and study both periodic and Dirichlet boundary conditions on cubes. We discuss the applications to the problem of finding quasi-periodic solutions. In the case of periodic boundary and the dimension n = 2, we apply KAM theory and prove the existence and stability of quasi-periodic solutions.
2010
Procesi, M. (2010). A normal form for beam and non-local nonlinear Schrodinger equations. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 43, 1-13 [10.1088/1751-8113/43/43/434028].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/133711
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 15
social impact