Reducible quasi-periodic solutions for the Non Linear Schrödinger equation

Abstract

The present paper is devoted to the construction of small reducible quasi--periodic solutions for the completely resonant NLS equations on a $d$--dimensional torus $\T^d$. The main point is to prove that prove that the normal form is reducible, block diagonal and satisfies the second Melnikov condition block wise. From this we deduce the result by a KAM algorithm.

48 pages

Cited by in corpus (5)

• Time quasi-periodic vortex patches of Euler equation in the plane
• KAM for beating solutions of the quintic NLS
• Long time stability of small finite gap solutions of the cubic Nonlinear Schrödinger equation on ${\mathbb{T}}^2$
• Long-time stability of the quantum hydrodynamic system on irrational tori
• An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation