Can one hear the full nonlinearity of a PDE from its small excitations?
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914006440083456 |
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| author | Olshanii, Maxim Boodhoo, Danshyl |
| author_facet | Olshanii, Maxim Boodhoo, Danshyl |
| contents | In this article, we show how one can restore an unknown nonlinear partial differential equation of a sine-Gordon type from its linearization around an unknown stationary kink. The key idea is to regard the ground state of the linear problem as the translation-related Goldstone mode of the nonlinear PDE sought after. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Can one hear the full nonlinearity of a PDE from its small excitations? Olshanii, Maxim Boodhoo, Danshyl Analysis of PDEs Quantum Gases Mathematical Physics In this article, we show how one can restore an unknown nonlinear partial differential equation of a sine-Gordon type from its linearization around an unknown stationary kink. The key idea is to regard the ground state of the linear problem as the translation-related Goldstone mode of the nonlinear PDE sought after. |
| title | Can one hear the full nonlinearity of a PDE from its small excitations? |
| topic | Analysis of PDEs Quantum Gases Mathematical Physics |
| url | https://arxiv.org/abs/2407.05215 |