Abstract
The initial value problem for a coupled nonlinear Schrödinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. In the focusing case, the existence and stability/instability of standing waves are established. Moreover, global well-posedness is discussed via the potential well method.
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Hezzi, H., Nour, M.M. & Saanouni, T. Coupled nonlinear Schrödinger equations with harmonic potential. Arab. J. Math. 7, 195–218 (2018). https://doi.org/10.1007/s40065-017-0192-2
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DOI: https://doi.org/10.1007/s40065-017-0192-2