학술논문
KAM for Beating Solutions of the Quintic NLS.
Document Type
Article
Author
Source
Subject
*KOLMOGOROV-Arnold-Moser theory
*SCHRODINGER equation
*NONLINEAR equations
*QUINTIC equations
*BIRKHOFF'S theorem (Relativity)
*FOURIER transforms
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Language
ISSN
0010-3616
Abstract
We consider the nonlinear Schrödinger equation of degree five on the circle $${\mathbb{T}= \mathbb{R} / 2\pi}$$ . We prove the existence of quasi-periodic solutions with four frequencies which bifurcate from 'resonant' solutions [studied in Grébert and Thomann (Ann Inst Henri Poincaré Anal Non Linéaire 29(3):455-477, 2012)] of the system obtained by truncating the Hamiltonian after one step of Birkhoff normal form, exhibiting recurrent exchange of energy between some Fourier modes. The existence of these quasi-periodic solutions is a purely nonlinear effect. [ABSTRACT FROM AUTHOR]