Abstract
Using the Feshbach resonance (FR) one can change a scattering length of two-body interactions and thus affect nonlinear dynamics of excitations in a Bose-Einstein condensate. The phenomenon is described by the Gross-Pitaevskii (GP) equation with varying nonlinearity. In this work we discuss the effect of variation of the nonlinearity on excitations in a BEC placed in an optical lattice. More specifically, we describe reductions of a three-dimensional (3D) GP equation to a 1D perturbed nonlinear Schrödinger (NLS) equation for different relations among parameters; discuss periodic solutions of the NLS equation; carry out numerical study of the dynamics of the NLS equation with a periodic and parabolic trap potentials. Special attention is paid to the process of generation of trains of bright and dark matter solitons from initially periodic waves.
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Brazhnyi, V., Konotop, V. (2004). Control of Matter Waves in Optical Lattices by Feshbach Resonance. In: Abdullaev, F.K., Konotop, V.V. (eds) Nonlinear Waves: Classical and Quantum Aspects. NATO Science Series II: Mathematics, Physics and Chemistry, vol 153. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2190-9_21
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DOI: https://doi.org/10.1007/1-4020-2190-9_21
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-2188-6
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