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

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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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Authors and Affiliations

  1. Department of Mathematics, University of Naples Federico II, Naples, 80138, Italy

    M. Procesi

  2. Department of Mathematics, University of Rome, La Sapienza, Rome, 00185, Italy

    C. Procesi

Authors
  1. M. Procesi
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  2. C. Procesi
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Correspondence to C. Procesi.

Additional information

Communicated by G. Gallavotti

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”.

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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

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