Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908854280781824 |
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| author | Rialland, Guillaume |
| author_facet | Rialland, Guillaume |
| contents | We consider perturbations of the one-dimensional cubic Schrödinger equation, under the form $i \, \partial_t ψ+ \partial_x^2 ψ+ |ψ|^2 ψ- g( |ψ|^2 ) ψ= 0$. Under hypotheses on the function g that can be easily verified in some cases, we show that the linearized problem around a solitary wave does not have internal mode (nor resonance) and we prove the asymptotic stability of these solitary waves, for small frequencies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01019 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes Rialland, Guillaume Analysis of PDEs We consider perturbations of the one-dimensional cubic Schrödinger equation, under the form $i \, \partial_t ψ+ \partial_x^2 ψ+ |ψ|^2 ψ- g( |ψ|^2 ) ψ= 0$. Under hypotheses on the function g that can be easily verified in some cases, we show that the linearized problem around a solitary wave does not have internal mode (nor resonance) and we prove the asymptotic stability of these solitary waves, for small frequencies. |
| title | Asymptotic stability of solitary waves for the 1D near-cubic non-linear Schrödinger equation in the absence of internal modes |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.01019 |