The singular perturbation limit of a variational problem from nonlinear fiber optics

Physica D: Nonlinear Phenomena

Volumn 180, Issue 1-2, 2003, Pages 108-114

  Kunze, Markus ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Dispersion managed solitons; Nonlocal variational problem; Singular perturbation

Indexed keywords

ELECTROMAGNETIC DISPERSION; FIBER OPTICS; PERTURBATION TECHNIQUES; SOLITONS; VARIATIONAL TECHNIQUES;

RESIDUAL DISPERSION;

NONLINEAR OPTICS;

EID: 0037947612     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(03)00066-6     Document Type: Article

References (23)

1. M. Ablowitz, G. Biondini, Multiscale pulse dynamics in communication systems with strong dispersion management, Opt. Lett. 23 (1998).
2. Th. Cazenave, An Introduction to Nonlinear Schrödinger Equations, 3rd ed., Instituto de Mathematica - UFJR, Rio de Janeiro, RJ, 1996. http://www.ann.jussieu.fr/̃cazenave/List_Art_Tele.html
3. A. Chraplyvy, et al., 8X10 GB/s transmission through 280 km of dispersion managed fiber, IEEE Photonics Tech. Lett. 5 (1993) 1233-1235.
4. Davey R.P., Smith K., McGuire A., Electr. Lett. 28:1992;482.
5. Gabitov I., Turitsyn S.K., Averaged pulse dynamics in the cascaded transmission system based on passive compensation technique. Opt. Lett. 21:1996;327-329.
6. A. Hasegawa, Y. Kodama, Solitons in Optical Communications, Oxford University Press, Oxford, New York, 1995.
7. R. Jackson, C.K.R.T. Jones, V. Zharnitsky, Critical points in the averaged variational principle for dispersion managed solitons, in preparation.
8. Kuisenga D.J., Siegman A.E., IEEE J. Quantum Electr. 6:1970;694.
9. Kunze M., Bifurcation from the essential spectrum without sign condition on the nonlinearity for a problem arising in optical fiber communication systems. Proc. Roy. Soc. Edinburgh Ser. A. 131:2001;927-943.
10. M. Kunze, On a variational problem with lack of compactness related to the nonlinear Schrödinger equation, submitted for publication.
11. Kunze M., Küpper T., Mezentsev V.K., Shapiro E.G., Turitsyn S., Nonlinear solitary waves with Gaussian tails. Physica D. 128:1999;273-295.
12. Lin C., Kogelnik H., Cohen L.G., Optical pulse equalization and low dispersion transmission in single-mode fibers in the 1.3-1.7 mm spectral region. Opt. Lett. 5:1980;476-478.
13. Lushnikov P.M., Dispersion-managed soliton in optical fibers with zero average dispersion. Opt. Lett. 25:2000;1144-1146.
14. Lushnikov P.M., On the boundary of the dispersion-managed soliton existence. JETP Lett. 72:2000;111-114.
15. Mezentsev V.K., Turitsyn S.K., Solitons with Gaussian tails in dispersion-managed communication systems using gratings. Phys. Lett. A. 237:1997;37-42.
16. Nakazawa M., Kubota H., Suzuki K., Yamada E., Recent progress in soliton transmission technology. Chaos. 10:2000;486-514.
17. Ni W.-M., Takagi I., Wei J., On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: intermediate solutions. Duke Math. J. 94:1998;597-618.
18. Nijhof J.H., Doran N.J., Forysiak W., Knox F.M., Stable soliton-like propagation in dispersion managed systems with net anomalous, zero, and normal dispersion. Electr. Lett. 33:1997;1726-1728.
19. H. Toda, K. Hamada, Y. Furukawa, Y. Kodama, S. Seikai, Experimental evaluation of Gordon-Haus timing jitter of dispersion managed solitons, in: Proceedings of the 25th European Conference on Optical Communication (ECOC'99), vol. 1, 1999, pp. 406-407.
20. Turitsyn S.K., Aceves A.B., Jones C.K.R.T., Zharnitsky V., Average dynamics of the optical soliton in communication lines with dispersion management: analytical results. Phys. Rev. E. 58:1998;R48-R51.
21. Turitsyn S.K., Aceves A.B., Jones C.K.R.T., Zharnitsky V., Mezentsev V.K., Hamiltonian averaging in soliton-bearing systems with a periodically varying dispersion. Phys. Rev. E. 59:1999;3843-3846.
22. Turitsyn S.K., Mezentsev V.K., Shapiro E.G., Dispersion-managed solitons and optimization of the dispersion management. Opt. Fiber Technol. 4:1998;384-452.
23. Zharnitsky V., Grenier E., Jones C.K.R.T., Turitsyn S.K., Stabilizing effects of dispersion management. Physica D. 152-153:2001;794-817.