Multisoliton solutions for equivariant wave maps on a $2+1$ dimensional wormhole
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912183869243392 |
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| author | Bizoń, Piotr Jendrej, Jacek Maliborski, Maciej |
| author_facet | Bizoń, Piotr Jendrej, Jacek Maliborski, Maciej |
| contents | We study equivariant wave maps from the $2+1$ dimensional wormhole to the 2-sphere. This model has explicit harmonic map solutions which, in suitable coordinates, have the form of the sine-Gordon kinks/anti-kinks. We conjecture that there exist asymptotically static chains of $N\geq 2$ alternating kinks and anti-kinks whose subsequent rates of expansion increase in geometric progression as $t\rightarrow \infty$. Our argument employs the method of collective coordinates to derive effective finite-dimensional ODE models for the asymptotic dynamics of $N$-chains. For $N=2,3$ the predictions of these effective models are verified by direct PDE computations which demonstrate that the $N$-chains lie at the threshold of kink-anti-kink annihilation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02020 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multisoliton solutions for equivariant wave maps on a $2+1$ dimensional wormhole Bizoń, Piotr Jendrej, Jacek Maliborski, Maciej Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics Pattern Formation and Solitons We study equivariant wave maps from the $2+1$ dimensional wormhole to the 2-sphere. This model has explicit harmonic map solutions which, in suitable coordinates, have the form of the sine-Gordon kinks/anti-kinks. We conjecture that there exist asymptotically static chains of $N\geq 2$ alternating kinks and anti-kinks whose subsequent rates of expansion increase in geometric progression as $t\rightarrow \infty$. Our argument employs the method of collective coordinates to derive effective finite-dimensional ODE models for the asymptotic dynamics of $N$-chains. For $N=2,3$ the predictions of these effective models are verified by direct PDE computations which demonstrate that the $N$-chains lie at the threshold of kink-anti-kink annihilation. |
| title | Multisoliton solutions for equivariant wave maps on a $2+1$ dimensional wormhole |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2410.02020 |