Orbitally stable standing waves for a system of coupled nonlinear Schrödinger equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 42, Issue 3, 2000, Pages 445-461

  Cipolatti, R ^a   Zumpichiatti, W ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Homogeneous; Orbital stability; Schr dinger equation; Standing waves

Indexed keywords

ASYMPTOTIC STABILITY; LAGRANGE MULTIPLIERS; NONLINEAR EQUATIONS; ONE DIMENSIONAL; ORDINARY DIFFERENTIAL EQUATIONS; SET THEORY;

HILBERT SPACES; MONOCHROMATIC WAVES; ORBITAL STABILITY; SCHRODINGER EQUATIONS; SOBOLEV SPACES; STANDING WAVES;

NONLINEAR SYSTEMS;

EID: 0034299686     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00357-5     Document Type: Article

References (15)

1. J. Bergh, J. Löfström, Interpolation Spaces, Springer, New York, 1976.
2. A.L. Berkhoer, V.E. Zakharov, Self exitation of waves with different polarizations in nonlinear media, Sov. Phys. JETP 31 (1970) 486-490.
3. T. Cazenave, An introduction to nonlinear Schrödinger equations, Textos de Métodos Matemáticos, Instituto de Matemática - UFRJ, vol. 26, 1993.
4. T. Cazenave, Blow up and scattering in the nonlinear Schrödinger equations, Textos de Métodos Matemáticos, Instituto de Matemática - UFRJ, vol. 30, 1994.
5. T. Cazenave, P.L. Lions, Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys. 85 (1982) 549-561.
6. R. Cipolatti, On the existence of standing waves for a Davey-Stewartson system, Commun. Partial Differential Equations 17(5&6) (1992) 967-988.
7. R. Cipolatti, W. Zumpichiatti, On the existence and regularity of ground states for a nonlinear system of coupled Schrödinger equations in ℝN, to appear.
8. A.S. Davidov, Solitons in quasi-one-dimensional molecular structures, Sov. Phys. Usp. 25(12) (1982) 298-918.
9. Y.S. Kivshar, B.A. Malomed, Many particles effects in nearly integrable systems, Physica 24D (1987) 125-154.
10. P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case, Part 1, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 109-145.
11. P.-L. Lions, The concentration-compactness principle in the calculus of variation. The locally compact case, Part 2, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 223-283.
12. S.V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Sov. Phys. JETP (38) (1974) 248-253.
13. G.K. Newbould, D.F. Parker, T.R. Faulkner, Coupled nonlinear Schrödinger equations arising in the study of monomode step-index optical fibers, J. Math. Phys. (30) (1989) 930-936.
14. M. Ohta, Stability of solitary waves for coupled nonlinear Schrödinger equations, Nonlinear Anal. 26(5) (1996) 933-939.
15. E.S.P. Siqueira, Asymptotic behavior of the solutions of a nonlinear system of Schrödinger equations, Nonlinear Anal. 20(10) (1993) 1231-1243.