Vortex Rings Pinning for the Gross-pitaevskii Equation in Three Dimensional Space
نویسندگان
چکیده
We construct traveling wave solutions possessing multiple stationary vortex rings with neighboring interaction to the problem iût = ε 2 4 û + ( Ṽ − |û| ) û, û ∈ H(R), where the unknown function û is defined as û : R3 ×R→ C, ε is a small positive parameter and Ṽ is a smooth potential. We first consider the case for two rings lying the same plane in a such way that they have interaction in the normal direction, which will be balanced by the role of trap potential. We also construct two parallel vortex rings which are trapped by the potential Ṽ so that they have balance of interaction in the binormal direction.
منابع مشابه
Vortex Ring Pinning for the Gross-Pitaevskii Equation in Three-Dimensional Space
We construct stationary solutions possessing two vortex rings to the nonlinear Schrödinger type problem iut = −ε4u + ( V + |u| ) u, where the unknown function u is defined as u : R3×R→ C, ε is a small positive parameter and V is a real smooth potential. These two vortex rings will be pinned at a fixed site by the potential V . They lie in the same plane and have neighboring interaction in the n...
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