Coupled Nonlinear Schrödinger Equations with a Gauge Potential: Existence and Blowup

We study solutions of the Cauchy problem for nonlinear Schrodinger 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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