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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.14223 |
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| _version_ | 1866914895225683968 |
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| author | Liu, Jiaqi Xu, XiXi |
| author_facet | Liu, Jiaqi Xu, XiXi |
| contents | We study the long time dynamics of the defocussing NLS equation. Compared with previous literature, we revisit the direct and inverse scattering map to obtain asymptotics in some weighted energy space that requires less restrictive decay and regularity assumptions. The main result is derived from an application of uniform resolvent bound and an approximation argument in the spirit of Riemann-Lebesgue lemma. As a consequence, our result depicts the long time dynamics of the zeros of the solution to the defocussing NLS equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14223 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial mass dynamics of the defocussing nonlinear Schrödinger equation Liu, Jiaqi Xu, XiXi Analysis of PDEs 35Q55 We study the long time dynamics of the defocussing NLS equation. Compared with previous literature, we revisit the direct and inverse scattering map to obtain asymptotics in some weighted energy space that requires less restrictive decay and regularity assumptions. The main result is derived from an application of uniform resolvent bound and an approximation argument in the spirit of Riemann-Lebesgue lemma. As a consequence, our result depicts the long time dynamics of the zeros of the solution to the defocussing NLS equation. |
| title | Partial mass dynamics of the defocussing nonlinear Schrödinger equation |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2407.14223 |