@article{faou:hal-00622240, TITLE = {{Sobolev stability of plane wave solutions to the cubic nonlinear Schr{\"o}dinger equation on a torus}}, AUTHOR = {Faou, Erwan and Gauckler, Ludwig and Lubich, Christian}, URL = {https://hal.archives-ouvertes.fr/hal-00622240}, JOURNAL = {{Communications in Partial Differential Equations}}, PUBLISHER = {{Taylor \& Francis: STM, Behavioural Science and Public Health Titles}}, VOLUME = {38}, NUMBER = {7}, PAGES = {1123-1140}, YEAR = {2013}, DOI = {10.1080/03605302.2013.785562}, KEYWORDS = {Nonlinear Schr{\"o}dinger equation ; Normal form ; Modulated Fourier expansion}, HAL_ID = {hal-00622240}, HAL_VERSION = {v2}, }