Artículos de revistas
Solutions To The Nonlinear Schrödinger Equation Carrying Momentum Along A Curve
Registro en:
Comptes Rendus Mathematique. , v. 346, n. 1-2, p. 33 - 38, 2008.
1631073X
10.1016/j.crma.2007.11.008
2-s2.0-38749119799
Autor
Mahmoudi F.
Malchiodi A.
Montenegro M.
Institución
Resumen
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. 346 1-2 33 38 Ambrosetti, A., Malchiodi, A., Perturbation Methods and Semilinear Elliptic Problems on Rn (2005) Progr. Math., 240. , Birkhäuser Ambrosetti, A., Malchiodi, A., Ni, W.M., Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I (2003) Commun. Math. Phys., 235, pp. 427-466 D'Aprile, T., On a class of solutions with non vanishing angular momentum for nonlinear Schrödinger equation (2003) Differential Integral Equations, 16 (3), pp. 349-384 Del Pino, M., Kowalczyk, M., Wei, J., Concentration at curves for nonlinear Schrödinger equations (2007) Comm. Pure Appl. Math., 60 (1), pp. 113-146 Mahmoudi, F., Malchiodi, A., Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem (2003) Rend. Lincei Mat. Appl., 17 (2006), pp. 279-290 Mahmoudi, F., Malchiodi, A., Concentration on minimal submanifolds for a singularly perturbed Neumann problem (2007) Adv. Math., 209, pp. 460-525 Malchiodi, A., Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains (2005) GAFA, 15 (6), pp. 1162-1222 Malchiodi, A., Montenegro, M., Boundary concentration phenomena for a singularly perturbed elliptic problem (2002) Comm. Pure Appl. Math., 55 (12), pp. 1507-1568 Malchiodi, A., Montenegro, M., Multidimensional boundary-layers for a singularly perturbed Neumann problem (2004) Duke Math. J., 124 (1), pp. 105-143 Mazzeo, R., Pacard, F., Foliations by constant mean curvature tubes (2005) Comm. Anal. Geom., 13 (4), pp. 633-670 Ni, W.M., Diffusion, cross-diffusion, and their spike-layer steady states (1998) Notices Amer. Math. Soc., 45 (1), pp. 9-18 Weinstein, A., Nonlinear stabilization of quasimodes (1980) Proc. Sympos. Pure Math., XXXVI, pp. 301-318. , Geometry of the Laplace Operator. Univ. Hawaii, Honolulu, Hawaii, 1979, Amer. Math. Soc., Providence, RI MR0573443 (82d:58016)