- 04-238 Guido Gentile and Michela Procesi
- Conservation of resonant periodic solutions for the
one-dimensional nonlinear Schroedinger equation
Aug 2, 04
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Abstract. We consider the one-dimensional nonlinear Schr\"odinger equation
with Dirichlet boundary conditions in the fully
resonant case (absence of the zero-mass term).
We investigate conservation of small amplitude periodic-solutions
for a large set measure of frequencies. In particular we show that
there are infinitely many periodic solutions which continue
the linear ones involving an arbitrary number of resonant modes,
provided the corresponding frequencies are large enough
and close enough to each other (wave packets with large wave number).