A Survey on Systems of Nonlinear Schrödinger Equations
Ambrosetti, Antonio
Bollettino dell'Unione Matematica Italiana, Tome 1 (2008), p. 475-486 / Harvested from Biblioteca Digitale Italiana di Matematica

We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.

Publié le : 2008-06-01
@article{BUMI_2008_9_1_2_475_0,
     author = {Antonio Ambrosetti},
     title = {A Survey on Systems of Nonlinear Schr\"odinger Equations},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {1},
     year = {2008},
     pages = {475-486},
     zbl = {1213.34109},
     mrnumber = {2424305},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_2_475_0}
}
Ambrosetti, Antonio. A Survey on Systems of Nonlinear Schrödinger Equations. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 475-486. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_2_475_0/

[1] Akhmediev, N. - Ankiewicz, A., Solitons, Nonlinear pulses and beams, Chapman and Hall, London, 1997.

[2] Akhmediev, N. - Ankiewicz, A., Novel soliton states and bifurcation phenomena in nonlinear fiber couplers, Phys. Rev. Lett., 70 (1993), 2395-2398. | MR 1212560 | Zbl 1063.35526

[3] Ambrosetti, A., A Note on nonlinear Schrödinger systems: existence of a-symmetric solutions, Adv. Nonlin. Studies, 6 (2006), 149-155. | MR 2172811 | Zbl 1113.34023

[4] Ambrosetti, A., Remarks on some systems of nonlinear Schrödinger equations, J. fixed point theory appl., DOI 10.1007/s11784-007-0035-4. | MR 2447960

[5] Ambrosetti, A. - Cerami, G. - Ruiz, D., Solitons of linearly coupled systems of semilinear non-autonomous equations on n , J. Funct. Anal., to appear. | MR 2414222 | Zbl 1148.35080

[6] Ambrosetti, A. - Colorado, E., Standing waves of some coupled nonlinear Schrödinger equations, Jour. London Math. Soc., 75 (2007), 67-82. | MR 2302730

[7] Ambrosetti, A. - Colorado, E. - Ruiz, D., Multi-bump solitons to linearly coupled NLS systems, Calc. Var. PDE, 30 (2007), 85-112. | MR 2333097 | Zbl 1123.35015

[8] Ambrosetti, A. - Malchiodi, A., Perturbation methods and semilinear elliptic problems on n , Progress in Math. Vol., 240, Birkhauser, 2005. | MR 2186962

[9] Benci, V. - Cerami, G., Positive Solutions of Some Nonlinear Elliptic Problems in Exterior Domains, Arch. Rat. Mech. Anal. 99 (1987), 283-300. | MR 898712 | Zbl 0635.35036

[10] Cazenave, T. - Lions, P. L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys., 85, no. 4 (1982), 549-561. | MR 677997 | Zbl 0513.35007

[11] Cerami, G., Some nonlinear elliptic problems in unbounded domains, Milan J. Math., 74 (2006), 47-77. | MR 2278729 | Zbl 1121.35054

[12] Cerami, G. - Passaseo, D., The effect of concentrating potentials in some singularly perturbed problems, Calc. Var. PDE, 17 (3) (2003), 257-281. | MR 1989833 | Zbl 1290.35050

[13] Cipollatti, R. - Zumpicchiatti, W., Orbitally stable standing waves for a system of coupled nonlinear Schrödinger equations, Nonlinear Anal. T.M.A., 42, no. 3 (2000), 445-461. | MR 1774273

[14] De Figueiredo, D. G. - Lopes, O., Solitary waves for some nonlinear Schrödinger systems, Ann. I.H.P. - Anal. non Linéaire, 25, no. 3 (2008), 149-161. | MR 2383083 | Zbl 1135.35072

[15] Maia, L. - Montefusco, E. - Pellacci, B., Positive solutions of a weakly coupled nonlinear Schrödinger system, J. Diff. Equat., 229 (2006), 743-767. | MR 2263573 | Zbl 1104.35053

[16] Montefusco, E. - Pellaccci, B. - Squassina, M., Semiclassical states for weakly coupled nonlinear Schrödinger system, J. Eur. Math. Soc., 10 (2008), 47-71. | MR 2349896

[17] Pomponio, A., Coupled nonlinear Schrödinger systems with potentials, J. Diff. Equations, 227 (2006), 258-281. | MR 2233961 | Zbl 1100.35098

[18] Stuart, C., Uniqueness and stability of ground states for some nonlinear Schrödinger equations, J. Eur. Math. Soc. (JEMS) 8, no. 2 (2006), 399-414. | MR 2239285