Quasi-periodic solutions of the Schrödinger equation with arbitrary algebraic nonlinearities

Details Quasi-periodic solutions of the Schrödinger equation with arbitrary algebraic nonlinearities Quasi-periodic solutions of the Schrödinger equation with arbitrary algebraic nonlinearities

2009-07-20

arxiv.org/abs/0907.3409v2

Mathematics

Analysis of PDEs

19 pp, slightly more details on proofs of Theorems 2 and 3

Scientific paper

We present a geometric formulation of existence of time quasi-periodic solutions. As an application, we prove the existence of quasi-periodic solutions of $b$ frequencies, $b\leq d+2$, in arbitrary dimension $d$ and for arbitrary non integrable algebraic nonlinearity $p$. This reflects the conservation of $d$ momenta, energy and $L^2$ norm. In 1d, we prove the existence of quasi-periodic solutions with arbitrary $b$ and for arbitrary $p$, solving a problem that started Hamiltonian PDE.

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