Blow-up criteria for the 1D NLS with combined nonlinearities
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912923351252992 |
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| author | Rodriguez, Alex D |
| author_facet | Rodriguez, Alex D |
| contents | In this paper we develop two different types of criteria for the finite time blow-up solutions to the combined nonlinear Schrödinger equation in 1D. The first one is a negative energy criterion developed for triple combined nonlinearity and then for a (convergent) infinite sum of combined nonlinearities, including an exponential nonlinearity. The second one is a positive energy criterion for the double nonlinearity with the defocusing-focusing coefficients. We also provide examples of initial data that satisfy either of the criteria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21040 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blow-up criteria for the 1D NLS with combined nonlinearities Rodriguez, Alex D Analysis of PDEs 35B44, 35Q40, 35Q55, 35A21 In this paper we develop two different types of criteria for the finite time blow-up solutions to the combined nonlinear Schrödinger equation in 1D. The first one is a negative energy criterion developed for triple combined nonlinearity and then for a (convergent) infinite sum of combined nonlinearities, including an exponential nonlinearity. The second one is a positive energy criterion for the double nonlinearity with the defocusing-focusing coefficients. We also provide examples of initial data that satisfy either of the criteria. |
| title | Blow-up criteria for the 1D NLS with combined nonlinearities |
| topic | Analysis of PDEs 35B44, 35Q40, 35Q55, 35A21 |
| url | https://arxiv.org/abs/2602.21040 |