DYNAMIC OF ONE DIMENSIONAL WAVE PACKET IN HIGH-ORDER APPROXIMATIONS OF NONLINEAR DISPERSION THEORY
Mots-clés :
High-order nonlinear Schrödinger equation, soliton, optical fiber.Résumé
We are interested by the soliton state solutions of the higher order nonlinear Schrödinger equation which
models the propagation of solitons in optical fibers. This nonlinear wave equation is solved by using the coupled
amplitude-phase formulation. These gives rise to a coupled pair of equations, which describe the interaction and
dynamics between the amplitude and the phase of the pulse. Integrating one of them, a characteristic equation is
derived. For different particular cases of the dependent nonlinear parameters, various types of soliton solutions
are investigated. In the absence of the third-order dispersion, we have obtained two different families of solitons:
bright soliton in anomalous-dispersion regime and dark soliton in normal dispersion regime. Other family of
bright solitons which is characterized by a simple quadratic dependence of the soliton phase on its amplitude, is
obtained when the third-order dispersion effect is zero. It is specifically investigated the dynamics of solitons in
the presence of third-order dispersion which is well described by the Korteweg-de Vries nonlinear equation.
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Références
- Enz U., Hev. Phys. Aota, 37, (1964), p. 245.
- Krumhansi J.A. and Schrieffer J.R., Phys. Rev. B11, (1975),
p. 3535; Koehler T.R., Bishop A.R., Schrieffer J.R., Solid
state Commun., 15, (1975), p. 1515.
- Kazumi Maki and Hiromichi Ebisawa, J. Low Temp. Phys.,
, (1976), p. 351; Kazumi Maki and Pradeep Kumar, Phys.
Rev. B, 14, (1976), p. 118; (1979), p. 3928.
- Nakajima K., Sawada Y. and Onodera Y., J. Appl. Phys., 46,
(1975), p.5272.
- Rice M.J., Bishop A.R., Krumhansi J.A., and Trullinger S.E.,
Phys. Rev. Lett., 36, (1976), p.432.
- Korteweg D.J. and de Vries G., “On the change of form of
long waves advancing in a rectangular canal, and on a new
type of long stationary waves”, Phil. Mag., 39, (1895), pp.
-443.
- Triki H., El Akrmi A., Rabia M.K., “Soliton solutions in
three linearly coupled Korteweg-de Vries equations”, Opt.
Commun., 201, (2002), pp. 447-455.
- Triki H., El Akrmi A., Rabia M.K., “Soliton states of ncoupled
Korteweg-de Vries equations”, Opt. Commun., 232,
(2004), pp. 429-437.
- Garnier J., “Long-time dynamics of Korteweg-de Vries
solitons driven by random perturbations”, Journal of
Statistical Physics, Vol. 105, N°516, (2001), pp. 789-833.
- Lamb G.L. and McLaughlin D.W., “Aspects of soliton
physics”, in "Solitons", R.K. Bullough and P.J. Candrey,
Eds., New York: Springer-Verlag, (1980), pp. 65-106.
- Gedalin M., Scott T.C., and Band Y.B., Phys. Rev. Lett., 78,
N°3, (1997), pp. 448-451.
- Fogel M.B., Trullinger S.E., Bihop A.R., and Krumhansi
J.A., Phys. Rev. B, 3, vol.15, (1976).
- Yuri S. Kivshar, Dmitry E. Pelinovsky, Thierry Cretegny,
and Michel Peyard, Phys. Rev. Lett., 80, N°23, (1998), pp.
-5035.
- Gromov E.M. and Talanov V.I., Zh. Eksp. Teor. Fiz., 110,
(1996), pp. 137-149.
- Min Du, Andrew K. Chan and Charles K. Chui, “A novel
approach to solving the nonlinear Schrödinger equation by
the coupled amplitude-phase formulation”, IEEE. J. Quant.
Elec., Vol. 31, N°1, (1995), p. 179.
- Y. Kodams, “Optical soliton in a monomode fiber”, J. Stat.
Phys., Vol. 39, (1985), p. 597.
- Hizanidis K. and Frantzekakis D.J., “Reductive perturbation
analysis of short pulse propagation in a nonlinear dielectric
slab: the role of material dispersion in bright to dark soliton
transitions”, IEEE. J. Quantum Electron., Vol. QE-29,
(1993), p. 286.
