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Solutions to the nonlinear Schrödinger equation carrying momentum along a curve
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Mahmoudi, Fethi, Malchiodi, A. and Montenegro, Marcelo (2008) Solutions to the nonlinear Schrödinger equation carrying momentum along a curve. Comptes Rendus Mathematique, Vol.346 (No.1-2). pp. 33-38. doi:10.1016/j.crma.2007.11.008 ISSN 1631073X.
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Official URL: http://dx.doi.org/10.1016/j.crma.2007.11.008
Abstract
We study the nonlinear Schrödinger equation −ε2Δψ+V(x)ψ=|ψ|p−1ψ on a compact manifold or on Rn, where V is a positive potential and p>1. As ε tends to zero, we prove existence of complex-valued solutions which concentrate along closed curves and whose phase is highly oscillatory, carrying quantum-mechanical momentum along the limit set.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Comptes Rendus Mathematique | ||||
Publisher: | Elsevier Masson | ||||
ISSN: | 1631073X | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.346 | ||||
Number: | No.1-2 | ||||
Page Range: | pp. 33-38 | ||||
DOI: | 10.1016/j.crma.2007.11.008 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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