Onset of Oscillations in Nonsoliton Pulses in Nonlinear Dispersive Fibers

Journal of Nonlinear Science

Volumn 8, Issue 1, 1998, Pages 43-62

  Forest, M G ^a   McLaughlin, K T R ^b  

^a University of North Carolina at Chapel Hill   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Hyperbolic shocks; Nonlinear dispersive fibers; Nonsoliton pulses; Onset of oscillations

Indexed keywords

EID: 0347468632     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329900043     Document Type: Article

References (27)

1. D. Anderson et al. J. Opt. Soc. Am., 10, 1185 (1993).
2. J. C. Bronski and D. W. McLaughlin. Semiclassical behavior in the NLS equation: Optical shocks-focusing instabilities. In Singular Limits of Dispersive Waves, N.M. Ercolani et al., ed., NATO ASI Series B 320, Plenum, New York, (1994).
3. P. Deift, K. T-R McLaughlin. A continuum limit of the Toda lattice. To appear, Memoirs of the AMS.
4. S. Evangelides. Private communication (August 1996).
5. M.G. Forest and J.-E. Lee. Geometry and modulation theory for the periodic nonlinear Schrödinger equation. IMA Volumes in Math. and Its Applications, D. Kinderlehrer et al., eds., 2, (1986).
6. E. Grenier. Limite Semi-Classique de l'equation de Schrödinger non lineare en temps petit. C. R. Acad. Sci. 320, 691-694 (1995).
7. A. Hasegawa and Y. Kodama. Opt. Lett., 15, 1443 (1990).
8. S. Jin. The semiclassical limit of the defocusing nonlinear Schrödinger flows. Ph.D. Thesis, University of Arizona (1991).
9. S. Jin, C.D. Levermore, and D.W. McLaughlin. The behavior of solutions of the NLS equation in the semi-classical limit. Singular Limits of Dispersive Waves, N.M. Ercolani et al., eds., NATO ASI Series B 320, Plenum, New York, 235-255 (1994).
10. Y. Kodama. Private communication; lecture at Notre Dame (April 1996).
11. Y. Kodama and S. Wabnitz. Analytic theory of guiding-center nonreturn-to-zero and return-to-zero signal transmission in normally dispersive nonlinear optical fibers. Opt. Lett., 20, 2291-2293 (1995).
12. P. Lax. Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys., 5, 611-613 (1965).
13. P. Lax, C.D. Levermore. The small dispersion limit of the Korteweg-de Vries equation I, II, III. Commun. Pure Appl. Math., 36, 253-290, 571-593, 809-829 (1983).
14. P. Lax, C.D. Levermore, and S. Venakides. The generation and propagation of oscillations in dispersive IVP's and their limiting behavior. Important Developments in Soliton Theory, T. Fokas and V.E. Zakharov, eds., Springer-Verlag, Berlin, (1992).
15. D. Marcuse. RMS width of pulses in nonlinear dispersive fibers. J. Lightwave Tech., 10, 17-21 (1992).
16. D. Marcuse, A Chraplyvy, and R. Tkach. Effect of fiber nonlinearity on long-distance transmission. J. Lightwave Tech., 9, 121-128 (1991).
17. K. T-R McLaughlin. A continuum limit of the Toda lattice. Ph.D. thesis, NYU (1994).
18. D.W. McLaughlin and J. A. Strain. Computing the weak limit of KdV. Commun. Pure Appl. Math., 47, 1319-1364 (1994).
19. L.F. Mollenauer, S.G. Evangelides, and H.A. Haus. J. Lightwave Tech., 9, 194 (1991).
20. J.E. Rothenberg and D. Grischkowsky. Observation of the formation of an optical intensity shock and wave breaking in the nonlinear propagation of pulses in optical fibers. Phys. Rev. Lett., 62, 531-534 (1989).
21. F.R. Tian. Oscillations of the zero dispersion limit of the Korteweg-de Vries equation. Commun. Pure Appl. Math., 46, 1093-1129 (1993).
22. F.R. Tian. Private communication (1996).
23. S. Venakides. The zero dispersion limit of the Korteweg-de Vries equation with nontrivial reflection coefficient. Commun. Pure Appl. Math., 38, 125-155 (1985).
24. S. Venakides. The generation of modulated wavetrains in the solution of the Korteweg-de Vries equation. Commun. Pure Appl. Math., 38, 883-909 (1985).
25. S. Venakides. The Korteweg-de Vries equation with small dispersion: Higher order Lax-Levermore theory. Commun. Pure Appl. Math.. 43, 335-361 (1990).
26. G.B. Whitham. Linear and Nonlinear Waves. Wiley Interscience, New York, 1974.
27. O. Wright. Korteweg-de Vries zero dispersion limit: A restricted initial value problem. Ph.D. Thesis, Princeton University (1991).