Stability of solitary waves for coupled nonlinear Schrödinger equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 26, Issue 5, 1996, Pages 933-939

  Ohta, Masahito ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Concentration compactness; Coupled nonlinear Schr dinger equations; Orbital stability; Solitary waves

Indexed keywords

EID: 0007078409     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00340-8     Document Type: Article

References (15)

1. NEWBOULT G. K., PARKER D. F. & FAULKNER T. R., Coupled nonlinear Schrödinger equations arising in the study of monomode step-index optical fibers, J. math. Phys. 30, 930-936 (1989).
2. WADATI M., IIZUKA T. & HISAKADO M., A coupled nonlinear Schrödinger equation and optical solitons, J. phys. Soc. Japan 61, 2241-2245 (1992).
3. GRILLAKIS M., SHATAH J. & STRAUSS W. A., Stability theory of solitary waves in the presence of symmetry, II, J. funct. Analysis 94, 308-348 (1990).
4. STUBBE J. & VÁZQUEZ L., A nonlinear Schrödinger equation with magnetic field effect: solitary waves with internal rotation, Portugaliae Math. 46, 493-499 (1989).
5. CAZENAVE T., An introduction to nonlinear Schrödinger equations, Textos de Métodos Matemáticos, Vol. 22. Instituto de Matemática - UFRJ, Rio de Janeiro (1989).
6. BERESTYCKI H. & CAZENAVE T., Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires, C. r. Acad. Sci. Paris 293, 489-492 (1981).
7. CAZENAVE T. & LIONS P.-L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Communs math. Phys. 85, 549-561 (1982).
8. GRILLAKIS M., SHATAH J. & STRAUSS W. A., Stability theory of solitary waves in the presence of symmetry, I, J. funct. Analysis 74, 160-197 (1987).
9. ILIEV I. D. & KIRCHEV K. P., Stability and instability of solitary waves for one-dimensional singular Schrödinger equations, Diff. Integral Eqns 6, 685-703 (1993).
10. SHATAH J., Stable standing waves of nonlinear Klein-Gordon equations, Communs math. Phys. 91, 313-327 (1983).
11. SHATAH J. & STRAUSS W. A., Instability of nonlinear bound states, Communs math. Phys. 100, 173-190 (1985).
12. WEINSTEIN M. I., Nonlinear Schrödinger equations and sharp interpolation estimates, Communs math. Phys. 87, 567-576 (1983).
13. WEINSTEIN M. I., Lyapunov stability of ground states of nonlinear dispersive evolution equations, Communs pure appl. Math. 39, 51-68 (1986).
14. LIONS P. L., The concentration-compactness principle in the calculus of variations. The locally compactness, part 1, Ann. Inst. H. Poincaré Analysis non linéaire 1, 109-145 (1984).
15. LIONS P. L., The concentration-compactness principle in the calculus of variations. The locally compactness, part 2, Ann. Inst. H. Poincaré Analysis non linéaire 1, 223-283 (1984).