We study the nonlinear Schrödinger equation - ε2 Δ ψ + V (x) ψ = | ψ |p - 1 ψ 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. To cite this article: F. Mahmoudi et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2007 Académie des sciences.
Solutions to the nonlinear Schrödinger equation carrying momentum along a curve
MALCHIODI, ANDREA;
2008
Abstract
We study the nonlinear Schrödinger equation - ε2 Δ ψ + V (x) ψ = | ψ |p - 1 ψ 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. To cite this article: F. Mahmoudi et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2007 Académie des sciences.File in questo prodotto:
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