arXiv:2304.02987 Abstract | arXiv Analytics

arXiv:2304.02987 [math.AP]Abstract References Reviews Resources

Quantized vortex dynamics of the nonlinear Schrödinger equation on torus with non-vanishing momentum

Published 2023-04-06Version 1

We derive rigorously the reduced dynamical laws for quantized vortex dynamics of the nonlinear Schr\"{o}dinger equation on torus with non-vanishing momentum when the vortex core size {\epsilon} \to 0. The reduced dynamical laws are governed by a Hamiltonian flow driven by a renormalized energy. A key ingredient is to construct a new canonical harmonic map to include the effect from the non-vanishing momentum into the dynamics. Finally, some properties of the reduced dynamical law are discussed.

Comments: 20 pages

Categories: math.AP

Subjects: 35Q40, 35Q55

Keywords: quantized vortex dynamics, nonlinear schrödinger equation, non-vanishing momentum, reduced dynamical law, hamiltonian flow driven

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