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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.09243 |
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| _version_ | 1866911501461225472 |
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| author | Hu, Shengqing Sun, Yingte |
| author_facet | Hu, Shengqing Sun, Yingte |
| contents | In this paper, we consider the following nonlinear disordered Stark model: $${\bf i}\partial_tu_n+δ(u_{n+1}+u_{n-1})+nu_n+v_nu_n+ε|u_n|^{2}u_n=0,\quad n\in\mathbb{Z}.$$ By employing the diagonalization of the associated linear operators and the KAM theory for nonlinear Hamiltonian systems, we establish that for parameters $δ$ and $\varepsilon$ in a reasonable range, and for most realization of random variables $v=\{v_n\}_{n \in \mathbb{Z}}$, there exist time quasi-periodic and spatially localized states that exhibit arbitrary power-law spatial decay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Localized state for nonlinear disordered stark model Hu, Shengqing Sun, Yingte Dynamical Systems In this paper, we consider the following nonlinear disordered Stark model: $${\bf i}\partial_tu_n+δ(u_{n+1}+u_{n-1})+nu_n+v_nu_n+ε|u_n|^{2}u_n=0,\quad n\in\mathbb{Z}.$$ By employing the diagonalization of the associated linear operators and the KAM theory for nonlinear Hamiltonian systems, we establish that for parameters $δ$ and $\varepsilon$ in a reasonable range, and for most realization of random variables $v=\{v_n\}_{n \in \mathbb{Z}}$, there exist time quasi-periodic and spatially localized states that exhibit arbitrary power-law spatial decay. |
| title | Localized state for nonlinear disordered stark model |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2603.09243 |