Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912380199370752 |
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| author | Eckhardt, Jonathan |
| author_facet | Eckhardt, Jonathan |
| contents | We show that solutions of the Korteweg-de Vries equation with reflectionless integrable initial data decompose into a (in general infinite) linear superposition of solitons after long enough time. The proof is based on a representation of reflectionless integrable potentials in terms of solutions to symmetric coupling problems for entire functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01878 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data Eckhardt, Jonathan Analysis of PDEs Primary 37K40, 35Q53, Secondary 37K15, 34L25 We show that solutions of the Korteweg-de Vries equation with reflectionless integrable initial data decompose into a (in general infinite) linear superposition of solitons after long enough time. The proof is based on a representation of reflectionless integrable potentials in terms of solutions to symmetric coupling problems for entire functions. |
| title | Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data |
| topic | Analysis of PDEs Primary 37K40, 35Q53, Secondary 37K15, 34L25 |
| url | https://arxiv.org/abs/2311.01878 |