On the cubic-quintic Schrödinger equation
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910824918941696 |
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| author | Baldelli, Laura |
| author_facet | Baldelli, Laura |
| contents | This paper explores the cubic-quintic Schrödinger equation in the entire Euclidean space. Our objectives are twofold: first, to advance the understanding of unresolved issues related to this equation, which are well known in the extensively studied Gross-Pitaevskii equation. Second, to consolidate existing results on the cubic-quintic equation, providing partial contributions. Specifically, we determine the explicit constant for the $L^\infty$ a priori bound and establish a partial existence result for finite energy traveling waves in suitable approximate domains of $\mathbb R^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the cubic-quintic Schrödinger equation Baldelli, Laura Analysis of PDEs 35Q55, 35Q40 This paper explores the cubic-quintic Schrödinger equation in the entire Euclidean space. Our objectives are twofold: first, to advance the understanding of unresolved issues related to this equation, which are well known in the extensively studied Gross-Pitaevskii equation. Second, to consolidate existing results on the cubic-quintic equation, providing partial contributions. Specifically, we determine the explicit constant for the $L^\infty$ a priori bound and establish a partial existence result for finite energy traveling waves in suitable approximate domains of $\mathbb R^d$. |
| title | On the cubic-quintic Schrödinger equation |
| topic | Analysis of PDEs 35Q55, 35Q40 |
| url | https://arxiv.org/abs/2502.09196 |