title: Bohr-Sommerfeld quantization condition for the Gross-Pitaevskii equation.
abstract: The discrete spectrum of the nonlinear eigenvalue problem associated to the one-dimensional Gross-Pitaevskii equation with a smooth potential is studied in the quasiclassical limit. We particularly focus on the corrections to the Bohr-Sommerfeld quantization rule for the excited energy levels due to the nonlinearity. Explicit predictions are obtained analytically for these corrections and are supported by numerical computations.
authors.affiliation: Departmento de Física, Universidade de Lisboa, Complexo Interdisciplinar, Avenida Professor Gama Pinto 2, Lisbon 1649-003, Portugal.
authors.forename: V V
authors.initials: VV
authors.lastname: Konotop
authors.forename: P G
authors.initials: PG
authors.lastname: Kevrekidis