Coupled Nonlinear Schrödinger Equations with a Gauge Potential: Existence and Blowup |
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| Authors: | João‐Paulo Dias Mário Figueira Vladimir V. Konotop |
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| Affiliation: | 1. CMAF‐CIO and FCUL;2. Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal |
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| Abstract: | We study solutions of the Cauchy problem for nonlinear Schrödinger system in  with nonlinear coupling and linear coupling modeling synthetic magnetic field in spin‐orbit coupled Bose–Einstein condensates. Three main results are presented: a proof of the local existence, a proof of the sufficient condition for the blowup result in finite time for some solutions, and the persistence of the nonlinear dynamics in the limit where the spin‐orbit coupling converges to zero. |
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