Existence of small semi-vortex solutions for the cubic nonlinear Schrödinger system with Rashba type Spin-Orbit coupling on $\mathbb{R}^2$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914495277826048 |
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| author | Inui, Takahisa |
| author_facet | Inui, Takahisa |
| contents | We consider the cubic nonlinear Schrödinger system with Rashba type Spin-Orbit coupling (SOC) on $\mathbb{R}^2$, which is also called the Gross--Pitaevskii equation with SOC. The system describes SO-coupled spinor BEC in physics. In the literature of physics, the existence of small semi-vortex solutions and small ground state is known. In the present paper, we give their mathematical proofs by finding minimizers of the energy under small mass constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19535 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of small semi-vortex solutions for the cubic nonlinear Schrödinger system with Rashba type Spin-Orbit coupling on $\mathbb{R}^2$ Inui, Takahisa Analysis of PDEs 35J10, 35J20, 35Q40 We consider the cubic nonlinear Schrödinger system with Rashba type Spin-Orbit coupling (SOC) on $\mathbb{R}^2$, which is also called the Gross--Pitaevskii equation with SOC. The system describes SO-coupled spinor BEC in physics. In the literature of physics, the existence of small semi-vortex solutions and small ground state is known. In the present paper, we give their mathematical proofs by finding minimizers of the energy under small mass constraint. |
| title | Existence of small semi-vortex solutions for the cubic nonlinear Schrödinger system with Rashba type Spin-Orbit coupling on $\mathbb{R}^2$ |
| topic | Analysis of PDEs 35J10, 35J20, 35Q40 |
| url | https://arxiv.org/abs/2604.19535 |