Existence and dependency results for coupled Schrödinger equations with critical exponent on waveguide manifold
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908707257843712 |
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| author | Wang, Jun Yin, Zhaoyang |
| author_facet | Wang, Jun Yin, Zhaoyang |
| contents | We study the coupled Schrödinger equations with critical exponent on $\mathbb{R}^3 \times \mathbb{T}$. With the help of scaling argument and semivirial-vanishing technology, we obtain the existence and $y$-dependence of solution, the tori can be generalized to $1$-dimensional compact Riemannian manifold. Moreover, the conclusion of this paper can be extended to systems with any number of components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and dependency results for coupled Schrödinger equations with critical exponent on waveguide manifold Wang, Jun Yin, Zhaoyang Analysis of PDEs We study the coupled Schrödinger equations with critical exponent on $\mathbb{R}^3 \times \mathbb{T}$. With the help of scaling argument and semivirial-vanishing technology, we obtain the existence and $y$-dependence of solution, the tori can be generalized to $1$-dimensional compact Riemannian manifold. Moreover, the conclusion of this paper can be extended to systems with any number of components. |
| title | Existence and dependency results for coupled Schrödinger equations with critical exponent on waveguide manifold |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.11491 |