Periodic solutions for a class of nonlinear partial differential equations in higher dimension

Abstract

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases where the bifurcation equation is infinite-dimensional, such as the nonlinear Schroedinger equation with zero mass, for which solutions which at leading order are wave packets are shown to exist.

34 pages

References in corpus (2)

• Periodic solutions for completely resonant nonlinear wave equations
• Conservation of resonant periodic solutions for the one-dimensional nonlinear Schroedinger equation

Cited by in corpus (5)

• A KAM algorithm for the resonant non--linear Schrödinger equation
• Normal Form for the Schrödinger equation with analytic non--linearities
• Quasi-periodic motions in dynamical systems. Review of a renormalisation group approach
• Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves
• The Existence of Periodic Solutions for Nonlinear Beam Equations on ${\mathbb{T}}^d$ by a Para-differential Method