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.
A normal form for beam and non-local nonlinear Schrodinger equations / Procesi, Michela. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - STAMPA. - 43:(2010), pp. 1-13. [10.1088/1751-8113/43/43/434028]
A normal form for beam and non-local nonlinear Schrodinger equations
PROCESI, Michela
2010
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.