TY - GEN A1 - Faou, Erwan A1 - Gauckler, Ludwig A1 - Lubich, Christian T1 - Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus N2 - It is shown that plane wave solutions to the cubic nonlinear Schrödinger equation on a torus behave orbitally stable under generic perturbations of the initial data that are small in a high-order Sobolev norm, over long times that extend to arbitrary negative powers of the smallness parameter. The perturbation stays small in the same Sobolev norm over such long times. The proof uses a Hamiltonian reduction and transformation and, alternatively, Birkhoff normal forms or modulated Fourier expansions in time. KW - nonlinear Schrödinger equation KW - plane wave KW - stability Y1 - 2013 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1188 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-11881 ER -