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

Abstract

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.

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Correspondence to C. Procesi.

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Supported by ERC grant “New connections between dynamical systems and Hamiltonian PDEs” and partially by the PRIN2009 grant “Critical Point Theory and Perturbative Methods for Nonlinear Differential Equations”.

Communicated by G. Gallavotti

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Procesi, M., Procesi, C. A Normal Form for the Schrödinger Equation with Analytic Non-linearities. Commun. Math. Phys. 312, 501–557 (2012). https://doi.org/10.1007/s00220-012-1483-2

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  • DOI: https://doi.org/10.1007/s00220-012-1483-2

Keywords

  • Normal Form
  • Cayley Graph
  • Geometric Realization
  • Geometric Graph
  • Black Vertex