A Survey on Systems of Nonlinear Schrödinger Equations
Bollettino dell'Unione Matematica Italiana (2008)
- Volume: 1, Issue: 2, page 475-486
- ISSN: 0392-4041
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topAmbrosetti, Antonio. "A Survey on Systems of Nonlinear Schrödinger Equations." Bollettino dell'Unione Matematica Italiana 1.2 (2008): 475-486. <http://eudml.org/doc/290487>.
@article{Ambrosetti2008,
abstract = {We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.},
author = {Ambrosetti, Antonio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {475-486},
publisher = {Unione Matematica Italiana},
title = {A Survey on Systems of Nonlinear Schrödinger Equations},
url = {http://eudml.org/doc/290487},
volume = {1},
year = {2008},
}
TY - JOUR
AU - Ambrosetti, Antonio
TI - A Survey on Systems of Nonlinear Schrödinger Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/6//
PB - Unione Matematica Italiana
VL - 1
IS - 2
SP - 475
EP - 486
AB - We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.
LA - eng
UR - http://eudml.org/doc/290487
ER -
References
top- AKHMEDIEV, N. - ANKIEWICZ, A., Solitons, Nonlinear pulses and beams, Chapman and Hall, London, 1997.
- AKHMEDIEV, N. - ANKIEWICZ, A., Novel soliton states and bifurcation phenomena in nonlinear fiber couplers, Phys. Rev. Lett., 70 (1993), 2395-2398. Zbl1063.35526MR1212560DOI10.1103/PhysRevLett.70.2395
- AMBROSETTI, A., A Note on nonlinear Schrödinger systems: existence of a-symmetric solutions, Adv. Nonlin. Studies, 6 (2006), 149-155. Zbl1113.34023MR2172811DOI10.1515/ans-2006-0202
- AMBROSETTI, A., Remarks on some systems of nonlinear Schrödinger equations, J. fixed point theory appl., DOI 10.1007/s11784-007-0035-4. MR2447960DOI10.1007/s11784-007-0035-4
- AMBROSETTI, A. - CERAMI, G. - RUIZ, D., Solitons of linearly coupled systems of semilinear non-autonomous equations on , J. Funct. Anal., to appear. Zbl1148.35080MR2414222DOI10.1016/j.jfa.2007.11.013
- AMBROSETTI, A. - COLORADO, E., Standing waves of some coupled nonlinear Schrödinger equations, Jour. London Math. Soc., 75 (2007), 67-82. MR2302730DOI10.1112/jlms/jdl020
- AMBROSETTI, A. - COLORADO, E. - RUIZ, D., Multi-bump solitons to linearly coupled NLS systems, Calc. Var. PDE, 30 (2007), 85-112. Zbl1123.35015MR2333097DOI10.1007/s00526-006-0079-0
- AMBROSETTI, A. - MALCHIODI, A., Perturbation methods and semilinear elliptic problems on , Progress in Math. Vol., 240, Birkhauser, 2005. MR2186962
- BENCI, V. - CERAMI, G., Positive Solutions of Some Nonlinear Elliptic Problems in Exterior Domains, Arch. Rat. Mech. Anal.99 (1987), 283-300. Zbl0635.35036MR898712DOI10.1007/BF00282048
- CAZENAVE, T. - LIONS, P. L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys., 85, no. 4 (1982), 549-561. Zbl0513.35007MR677997
- CERAMI, G., Some nonlinear elliptic problems in unbounded domains, Milan J. Math., 74 (2006), 47-77. Zbl1121.35054MR2278729DOI10.1007/s00032-006-0059-z
- CERAMI, G. - PASSASEO, D., The effect of concentrating potentials in some singularly perturbed problems, Calc. Var. PDE, 17 (3) (2003), 257-281. Zbl1290.35050MR1989833
- 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. MR1774273DOI10.1016/S0362-546X(98)00357-5
- 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. Zbl1135.35072MR2383083DOI10.1016/j.anihpc.2006.11.006
- MAIA, L. - MONTEFUSCO, E. - PELLACCI, B., Positive solutions of a weakly coupled nonlinear Schrödinger system, J. Diff. Equat., 229 (2006), 743-767. Zbl1104.35053MR2263573DOI10.1016/j.jde.2006.07.002
- MONTEFUSCO, E. - PELLACCCI, B. - SQUASSINA, M., Semiclassical states for weakly coupled nonlinear Schrödinger system, J. Eur. Math. Soc., 10 (2008), 47-71. MR2349896DOI10.4171/JEMS/103
- POMPONIO, A., Coupled nonlinear Schrödinger systems with potentials, J. Diff. Equations, 227 (2006), 258-281. Zbl1100.35098MR2233961DOI10.1016/j.jde.2005.09.002
- STUART, C., Uniqueness and stability of ground states for some nonlinear Schrödinger equations, J. Eur. Math. Soc. (JEMS) 8, no. 2 (2006), 399-414. MR2239285DOI10.4171/JEMS/60
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