Stability of bound states for regularized nonlinear Schrödinger equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909288075624448 |
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| author | Albert, John Arbunich, Jack |
| author_facet | Albert, John Arbunich, Jack |
| contents | We consider the stability of bound-state solutions of a family of regularized nonlinear Schrödinger equations which were introduced by Dumas, Lannes and Szeftel as models for the propagation of laser beams. Among these bound-state solutions are ground states, which are defined as solutions of a variational problem. We give a sufficient condition for existence and orbital stability of ground states, and use it to verify that ground states exist and are stable over a wider range of nonlinearities than for the nonregularized nonlinear Schrödinger equation. We also give another sufficient and almost necessary condition for stability of general bound states, and show that some stable bound states exist which are not ground states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of bound states for regularized nonlinear Schrödinger equations Albert, John Arbunich, Jack Analysis of PDEs 35Q55 (Primary) 35Q60, 35B35 (Secondary) We consider the stability of bound-state solutions of a family of regularized nonlinear Schrödinger equations which were introduced by Dumas, Lannes and Szeftel as models for the propagation of laser beams. Among these bound-state solutions are ground states, which are defined as solutions of a variational problem. We give a sufficient condition for existence and orbital stability of ground states, and use it to verify that ground states exist and are stable over a wider range of nonlinearities than for the nonregularized nonlinear Schrödinger equation. We also give another sufficient and almost necessary condition for stability of general bound states, and show that some stable bound states exist which are not ground states. |
| title | Stability of bound states for regularized nonlinear Schrödinger equations |
| topic | Analysis of PDEs 35Q55 (Primary) 35Q60, 35B35 (Secondary) |
| url | https://arxiv.org/abs/2408.08279 |