Well–posedness of dispersion managed nonlinear Schrödinger equations
We prove local and global well–posedness results for the Gabitov–Turitsyn or dispersion managed nonlinear Schrödinger equation with a large class of nonlinearities and arbitrary average dispersion on L2(R) and H1(R) for zero and non–zero average dispersions, respectively. Moreover, when the average...
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| Published in | Journal of mathematical analysis and applications Vol. 522; no. 1; p. 126938 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.06.2023
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| Abstract | We prove local and global well–posedness results for the Gabitov–Turitsyn or dispersion managed nonlinear Schrödinger equation with a large class of nonlinearities and arbitrary average dispersion on L2(R) and H1(R) for zero and non–zero average dispersions, respectively. Moreover, when the average dispersion is non–negative, we show that the set of ground states is orbitally stable. This covers the case of non–saturated and saturated nonlinear polarizations and yields, for saturated nonlinearities, the first proof of orbital stability. |
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| AbstractList | We prove local and global well–posedness results for the Gabitov–Turitsyn or dispersion managed nonlinear Schrödinger equation with a large class of nonlinearities and arbitrary average dispersion on L2(R) and H1(R) for zero and non–zero average dispersions, respectively. Moreover, when the average dispersion is non–negative, we show that the set of ground states is orbitally stable. This covers the case of non–saturated and saturated nonlinear polarizations and yields, for saturated nonlinearities, the first proof of orbital stability. |
| ArticleNumber | 126938 |
| Author | Hundertmark, Dirk Lee, Young-Ran Choi, Mi-Ran |
| Author_xml | – sequence: 1 givenname: Mi-Ran surname: Choi fullname: Choi, Mi-Ran email: mrchoi@sogang.ac.kr organization: Department of Mathematics, Sogang University, 35 Baekbeom-ro (Sinsu–dong), Mapo-gu, Seoul, 04107, South Korea – sequence: 2 givenname: Dirk surname: Hundertmark fullname: Hundertmark, Dirk email: dirk.hundertmark@kit.edu organization: Department of Mathematics, Institute for Analysis, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany – sequence: 3 givenname: Young-Ran orcidid: 0000-0001-6813-9058 surname: Lee fullname: Lee, Young-Ran email: younglee@sogang.ac.kr organization: Department of Mathematics, Sogang University, 35 Baekbeom-ro (Sinsu–dong), Mapo-gu, Seoul, 04107, South Korea |
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| Cites_doi | 10.1007/BF01403504 10.1007/s11005-015-0811-9 10.1353/ajm.1998.0039 10.1142/S0129055X17500222 10.1007/s00013-015-0731-z 10.1137/15M103666X 10.1215/S0012-7094-77-04430-1 10.1016/j.jde.2004.10.006 10.4310/MRL.2011.v18.n1.a2 10.1364/OL.21.000327 10.1364/OL.23.001668 10.1088/1361-6544/ac5464 10.1063/5.0053132 10.1016/j.jde.2017.08.028 10.1007/s00030-021-00731-6 10.1016/0022-1236(73)90051-7 10.1016/s0294-1449(16)30399-7 10.1088/1361-6544/aa6aad 10.1134/1.567103 10.1007/s00220-008-0612-4 10.1007/s00526-005-0349-2 10.1016/S0167-2789(01)00213-5 10.1016/j.physrep.2012.09.004 10.1007/s00332-011-9106-1 |
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| Keywords | Orbital stability Nonlocal NLS Dispersion management Well–posedness |
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| Snippet | We prove local and global well–posedness results for the Gabitov–Turitsyn or dispersion managed nonlinear Schrödinger equation with a large class of... |
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| SubjectTerms | Dispersion management Nonlocal NLS Orbital stability Well–posedness |
| Title | Well–posedness of dispersion managed nonlinear Schrödinger equations |
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