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A sufficient
condition for global existence of solutions to a generalized
derivative nonlinear Schrödinger equation
Noriyoshi Fukaya, Masayuki Hayashi and Takahisa Inui |
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Vol. 10 (2017), No. 5, 1149–1167
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Abstract |
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We give a sufficient condition for global existence of the solutions to a generalized derivative nonlinear Schrödinger equation (gDNLS) by a variational argument. The variational argument is applicable to a cubic derivative nonlinear Schrödinger equation (DNLS). For (DNLS), Wu (2015) proved that the solution with the initial data is global if by the sharp Gagliardo–Nirenberg inequality. The variational argument gives us another proof of the global existence for (DNLS). Moreover, by the variational argument, we can show that the solution to (DNLS) is global if the initial data satisfies and the momentum is negative. |
Keywords
variational structure, generalized derivative nonlinear
Schrödinger equation, global existence
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Mathematical Subject Classification 2010
Primary: 35Q55
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Milestones
Received: 8 October 2016
Revised: 28 February 2017
Accepted: 3 April 2017
Published: 1 July 2017
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Authors |
| Noriyoshi Fukaya | |
| Department of Mathematics Graduate School of Science Tokyo University of Science Shinjuku, Tokyo 162-8601 Japan |
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| Masayuki Hayashi | |
| Department of Applied Physics Waseda University Shinjuku, Tokyo 169-8555 Japan |
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| Takahisa Inui | |
| Department of Mathematics Graduate School of Science Kyoto University Kyoto City, Kyoto 606-8502 Japan |
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