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Stability of small
solitary waves for the one-dimensional NLS with an attractive
delta potential
Satoshi Masaki, Jason Murphy and Jun-ichi Segata |
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Vol. 13 (2020), No. 4, 1099–1128
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Abstract |
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We consider the initial-value problem for the one-dimensional nonlinear Schrödinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as . In particular, we establish the asymptotic stability of the family of small solitary waves. |
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Keywords
NLS, solitary waves, asymptotic stability, delta potential
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Mathematical Subject Classification 2010
Primary: 35Q55
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Milestones
Received: 31 July 2018
Revised: 28 January 2019
Accepted: 18 April 2019
Published: 13 June 2020
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Authors |
| Satoshi Masaki | |
| Department of Systems
Innovation Graduate School of Engineering Science Osaka University Osaka Japan |
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| Jason Murphy | |
| Department of Mathematics and
Statistics Missouri University of Science and Technology Rolla, MO United States |
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| Jun-ichi Segata | |
| Mathematical Institute Tohoku University Sendai Japan |
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