On the orbital stability of periodic snoidal waves for the $ϕ^4-$equation
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909971447283712 |
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| author | Lonardoni, B. S. Natali, F. |
| author_facet | Lonardoni, B. S. Natali, F. |
| contents | The main purpose of this paper is to investigate the global well-posedness and orbital stability of odd periodic traveling waves for the $ϕ^4$-equation in the Sobolev space of periodic functions with zero mean. We establish new results on the global well-posedness of weak solutions by combining a semigroup approach with energy estimates. As a consequence, we prove the orbital stability of odd periodic waves by applying a Morse index theorem to the constrained linearized operator defined in the Sobolev space with the zero mean property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the orbital stability of periodic snoidal waves for the $ϕ^4-$equation Lonardoni, B. S. Natali, F. Analysis of PDEs The main purpose of this paper is to investigate the global well-posedness and orbital stability of odd periodic traveling waves for the $ϕ^4$-equation in the Sobolev space of periodic functions with zero mean. We establish new results on the global well-posedness of weak solutions by combining a semigroup approach with energy estimates. As a consequence, we prove the orbital stability of odd periodic waves by applying a Morse index theorem to the constrained linearized operator defined in the Sobolev space with the zero mean property. |
| title | On the orbital stability of periodic snoidal waves for the $ϕ^4-$equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.05547 |