A Normal Form for the Schrödinger Equation with Analytic Non-linearities

By Michela Procesi, C. Procesi. 2010

73 citations recorded by the source corpus.

We discuss a class of normal forms of the completely resonant non-linear Schrödinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4e5548d9d6c0bfee983a55a7a1351b8fa9ce0c23

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Riccardo Montalto
2. Massimiliano Berti
3. Pierre Baldi
4. P. Bolle
5. R. Feola
6. Felice Iandoli

In Mathematical Physics

1. Massimiliano Berti
2. Riccardo Montalto
3. Pierre Baldi
4. P. Bolle
5. Michela Procesi
6. Ivar Ekeland
7. C. Procesi

In Statistical and Nonlinear Physics

1. Massimiliano Berti
2. Riccardo Montalto
3. Pierre Baldi
4. P. Bolle
5. Michela Procesi
6. R. Feola
7. E. Haus
8. Ivar Ekeland

Citations in the corpus

• KAM for autonomous quasi-linear perturbations of mKdV (2014, methodology): “For PDEs in higher space dimension the theory has been more recently extended by Bourgain [10], Eliasson–Kuksin [13], and Berti–Bolle [6], Geng–Xu–You [14], Procesi–Procesi [30,29], Wang [32].”
• Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential (2010, methodology): “For the cubic NLS in d = 2 the existence of quasi-periodic solutions has been recently proved by Geng–Xu–You [25] via a Birkhoff normal form and a modification of the KAM approach in [21] (see also Procesi–Procesi [36]), valid in any dimension.”