Bound and ground states of coupled nonlinear Schrödinger equations

Antonio Ambrosetti; Eduardo Colorado

doi:10.1016/j.crma.2006.01.024

Partial Differential Equations

Bound and ground states of coupled nonlinear Schrödinger equations
[Solutions à énergie finie et minimale d'équations de Schrödinger non linéaires couplées]

Présenté par : Haïm Brezis

Antonio Ambrosetti ¹ ; Eduardo Colorado ¹

¹ SISSA, 2-4, via Beirut, Trieste 34014, Italy

Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 453-458.

Résumé
Abstract

On montre l'existence de solutions à énergie finie et énergie minimale pour quelques systèmes couplés d'équations de Schrödinger non linéaires.

We prove existence of bound and ground states of some systems of coupled nonlinear Schrödinger equations.

Accepté le : 2006-01-20
Publié le : 2006-03-03

DOI : 10.1016/j.crma.2006.01.024

Affiliations des auteurs :

Antonio Ambrosetti ¹ ; Eduardo Colorado ¹

¹ SISSA, 2-4, via Beirut, Trieste 34014, Italy

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     author = {Antonio Ambrosetti and Eduardo Colorado},
     title = {Bound and ground states of coupled nonlinear {Schr\"odinger} equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {453--458},
     publisher = {Elsevier},
     volume = {342},
     number = {7},
     year = {2006},
     doi = {10.1016/j.crma.2006.01.024},
     language = {en},
}

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Antonio Ambrosetti; Eduardo Colorado. Bound and ground states of coupled nonlinear Schrödinger equations. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 453-458. doi : 10.1016/j.crma.2006.01.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.024/

Bibliographie
Cité par

[1] N. Akhmediev; A. Ankiewicz Solitons, Nonlinear Pulses and Beams, Chapman & Hall, London, 1997

[2] N. Akhmediev; A. Ankiewicz Novel soliton states and bifurcation phenomena in nonlinear fiber couplers, Phys. Rev. Lett., Volume 70 (1993) no. 16, pp. 2395-2398

[3] A. Ambrosetti, E. Colorado, Standing waves of some coupled nonlinear Schrödinger equations, in press

[4] A. Ambrosetti; A. Malchiodi Perturbation Methods and Semilinear Elliptic Problems on $R^{n}$ , Progr. in Math., vol. 240, Birkhäuser, 2005

[5] T.-C. Lin; J. Wei Ground state of N coupled nonlinear Schrödinger equations in $R^{n}$ , $n ⩽ 3$ , Comm. Math. Phys., Volume 255 (2005), pp. 629-653

[6] W.A. Strauss Existence of solitary waves in higher dimensions, Comm. Math. Phys., Volume 55 (1977), pp. 149-162

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