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arXiv · 1412.5786

Quasi-periodic solutions for fully nonlinear forced reversible Schroedinger equations

Roberto Feola·Michela Procesi
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Abstract

In this paper we consider a class of fully nonlinear forced and reversible Schroedinger equations and prove existence and stability of quasi-periodic solutions. We use a Nash-Moser algorithm together with a reducibility theorem on the linearized operator in a neighborhood of zero. Due to the presence of the highest order derivatives in the non-linearity the classic KAM-reducibility argument fails and one needs to use a wider class of changes of variables such has diffeomorphisms of the torus and pseudo-differential operators. This procedure automtically produces a change of variables, well defined on the phase space of the equation, which diagonalizes the operator linearized at the solution. This gives the linear stability.

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Roberto Feola, Michela Procesi. 2014-12-18. Quasi-periodic solutions for fully nonlinear forced reversible Schroedinger equations. https://doi.org/10.1016/j.jde.2015.04.025

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