In this paper we consider a class of fully nonlinear forced and reversible Schrödinger 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 as diffeomorphisms of the torus and pseudo-differential operators. This procedure automatically 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.
|Titolo:||Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations|
|Data di pubblicazione:||2015|
|Citazione:||Feola, R., & Procesi, M. (2015). Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations. JOURNAL OF DIFFERENTIAL EQUATIONS, 259(7), 3389-3447.|
|Appare nelle tipologie:||1.1 Articolo in rivista|