Quantized vortex dynamics of the complex Ginzburg-Landau equation on torus
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913400371544064 |
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| author | Zhu, Yongxing |
| author_facet | Zhu, Yongxing |
| contents | We derive rigorously the reduced dynamical laws for quantized vortex dynamics of the complex Ginzburg-Landau equation on torus when the core size of vortex $\varepsilon\to 0$. The reduced dynamical laws of the complex Ginzburg-Landau equation are governed by a mixed flow of gradient flow and Hamiltonian flow which are both driven by a renormalized energy on torus. Finally, some first integrals and analytic solutions of the reduced dynamical laws are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08301 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantized vortex dynamics of the complex Ginzburg-Landau equation on torus Zhu, Yongxing Analysis of PDEs Dynamical Systems We derive rigorously the reduced dynamical laws for quantized vortex dynamics of the complex Ginzburg-Landau equation on torus when the core size of vortex $\varepsilon\to 0$. The reduced dynamical laws of the complex Ginzburg-Landau equation are governed by a mixed flow of gradient flow and Hamiltonian flow which are both driven by a renormalized energy on torus. Finally, some first integrals and analytic solutions of the reduced dynamical laws are discussed. |
| title | Quantized vortex dynamics of the complex Ginzburg-Landau equation on torus |
| topic | Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2304.08301 |