Quasi Periodic Solutions of Nonlinear Random Schrödinger Equations
Quasi-periodic solutions for a nonlinear wave equation.
Quasi-periodic solutions of nonlinear random Schrödinger equations
Quasi-periodic solutions of PDEs
The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in , , and the - derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.
Quasi-periodic solutions with Sobolev regularity of NLS on with a multiplicative potential
We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on , finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are then the solutions are . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators...