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

Presented by: 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.

Abstract
Résumé

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

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

Accepted: 2006-01-20
Published online: 2006-03-03

DOI: 10.1016/j.crma.2006.01.024

Author's affiliations:

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/

References
Cited by

[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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