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arXiv · 2304.02987

Quantized vortex dynamics of the nonlinear Schr\"{o}dinger equation on torus with non-vanishing momentum

Yongxing Zhu·Weizhu Bao·Huaiyu Jian
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Abstract

We derive rigorously the reduced dynamical laws for quantized vortex dynamics of the nonlinear Schr\"{o}dinger equation on the 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.

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Yongxing Zhu, Weizhu Bao, Huaiyu Jian. 2023-04-06. Quantized vortex dynamics of the nonlinear Schr\"{o}dinger equation on torus with non-vanishing momentum. https://doi.org/10.1016/j.physd.2023.133812

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