Quartic normal forms for the periodic nonlinear Schrödinger equation with dispersion management

Physica D: Nonlinear Phenomena

Volumn 191, Issue 3-4, 2004, Pages 219-237

  Panayotaros, Panayotis ^a,b  

^a UNIVERSITY OF COLORADO   (United States)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

Nonlinear Schr dinger equations; Normal forms; Parametric forcing

Indexed keywords

DYNAMICS; GALERKIN METHODS; HAMILTONIANS; LIGHT TRANSMISSION; PARTIAL DIFFERENTIAL EQUATIONS;

NORMAL FORMS; PARAMETRIC FORCING;

NONLINEAR EQUATIONS;

EID: 1842736754     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2004.01.037     Document Type: Article

References (25)

1. Ablowitz M.R., Biondini G., Multiscale pulse dynamics in communication systems with strong dispersion management. Opt. Lett. 23:1998;1668-1670.
2. Bambusi D., Nekhoroshev estimates for small amplitude solutions in nonlinear Schrödinger equations. Math. Z. 230:1999;345-387.
3. Bambusi D., Carati A., Ponno A., The nonlinear Schrödinger equation as a resonant normal form. Disc. Cont. Dyn. Syst.-Ser. B. 2:2002;109-128.
4. Cautaerts V., Maruta A., Kodama Y., On the dispersion managed soliton. Chaos. 10:2003;515-528.
5. Gabitov I.R., Turytsin S.K., Averaged pulse dynamics in a cascaded transmission line with passive dispersion compensation. Opt. Lett. 21:1996;327-329.
6. S.B. Kuksin, Analysis of Hamiltonian PDEs, Oxford University Press, Oxford, 2000.
7. Kuksin S.B., Pöschel J., Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation. Ann. Math. 143:1996;149-179.
8. Kunze M., Bifurcation from the essential spectrum without sign condition on the nonlinearity. Proc. Roy. Soc. Edinburgh Sect. A. 131:2001;927-943.
9. M. Kunze, The singular perturbation limit of a variational problem from nonlinear fiber optics, Physica D, in press.
10. Kurtzke C., Suppression of fiber nonlinearities by appropriate dispersion management. IEEE Photon. Tech. Lett. 5:1993;1250-1253.
11. Lakoba T.I., Pelinovsky D.E., Persistent oscillations of scalar and vector dispersion managed solitons. Chaos. 10:2000;539-550.
12. Lakoba T.I., Yang J., Kaup D.J., Malomed B.A., Conditions for stationary pulse propagation in the strong dispersion management regime. Opt. Comm. 149:1998;366-375.
13. Moser J., Periodic orbits and a theorem by Alan Weinstein. Comm. Pure Appl. Math. 29:1976;727-747.
14. J. Moeser, C.K.R.T. Jones, V. Zharnitsky, I.R. Gabitov, Ground states for the nonlinear Schrödinger equation with higher order dispersion management, preprint, 2002.
15. Moeser J., Gabitov I., Jones C.K.R.T., Pulse stabilization by high-order dispersion management. Opt. Lett. 27:2002;2206-2208.
16. Matthies K., Scheel A., Exponential averaging for Hamiltonian evolution equations. Trans. AMS. 355:2002;747-773.
17. Nijhof J.H.B., 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.
18. J. Pöschel, E. Trubowitz, Inverse Spectral Theory, Academic Press, Boston, 1987.
19. Pöschel J., On Nekhoroshev estimates for a nonlinear Schrödinger equation and a theorem of Bambusi. Nonlinearity. 12:1999;1587-1600.
20. Smith N.J., Knox F.M., Doran N.J., Blow K.J., Bennion I., Enhanced power solitons in optical fibres with periodic dispersion management. Electr. Lett. 32:1996;54-55.
21. Turytsin S.K., Mezentsev V.K., On the theory of chirped optical solitons in fiber lines with varying dispersion. JETP Lett. 68:1998;830-836.
22. Yang T.S., Kath W.L., Radiation loss of dispersion-managed solitons in optical fibers. Physica D. 149:2001;80-94.
23. Yang T.S., Kath W.L., Turytsin S.K., The multiple scale averaging and dynamics of dispersion-managed optical solitons. J. Eng. Math. 36:1999;136-184.
24. Weinstein A., Normal modes for nonlinear Hamiltonian systems. Inv. Math. 20:1973;47-57.
25. Zharnitsky V., Grenier E., Jones C.K.R.T., Turytsin S.K., Stabilizing effect of dispersion management. Physica D. 152-153:2001;794-817.