|
SIGMA 3 (2007), 083, 9 pages arXiv:0708.3506
https://doi.org/10.3842/SIGMA.2007.083
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics
Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
Maxim A. Molchan
B.I. Stepanov Institute of Physics, 68 Nezalezhnasci Ave., 220072 Minsk, Belarus
Received July 26, 2007, in final form August 15, 2007; Published online August 26, 2007
Abstract
On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.
Key words:
nonlocality; competing nonlinearity; stochasticity.
pdf (1328 kb)
ps (1728 kb)
tex (2725 kb)
References
- Kivshar Yu.S., Luther-Davies B., Dark optical solitons: physics and applications, Phys. Rep. 298 (1998), 81-197.
- Mamyshev P.V., Bosshard C., Stegeman G.I., Generation of a periodic array of dark spatial solitons in the regime of effective amplification, J. Opt. Soc. Amer. B Opt. Phys. 11 (1994), 1254.
- Hasewaga A., Observation of self-trapping instability of a plasma cyclotron wave
in a computer experiment, Phys. Rev. Lett. 24 (1970), 1165-1168.
- Whitham G.B., Nonlinear dispersive waves, Proc. R. Soc. London A 283 (1965), 238-261.
- Benjamin T.B., Feir J.E., The disintegration of wave trains on deep water,
J. Fluid Mech. 27 (1967), 417-430.
- Wu B., Niu Q., Landau and dynamical instabilities of the superflow
of Bose-Einstein condensates in optical lattices, Phys.
Rev. A 64 (2001), 061603, 4 pages, cond-mat/0009455.
- Kevrekidis P.G., Frantzeskakis D.J., Pattern forming
dynamical instabilities of Bose-Einstein condensates,
Modern Phys. Lett. B 18 (2004), 173-202, cond-mat/0406657.
- Stegeman G.I., Segev M., Optical spatial solitons and
their interactions: universality and diversity, Science
286 (1999), 1518-1522.
- Tai K., Hasegawa A., Tomita A., Observation of modulational instability
in optical fibers, Phys. Rev. Lett. 56 (1986), 135-138.
- Kivshar Yu.S., Agraval G.P., Optical solitons:
from fibers to photonic crystals, Academic Press, San Diego, 2003.
- Abdullaev F.Kh., Darmanyan S.A., Garnier J., Modulational
instability of electromagnetic waves in inhomogeneous and in
discrete media, Progr. Opt. 44 (2002), 303-365.
- Peccianti M., Conti C., Alberici E., Assanto G., Spatially incoherent modulational instability in a nonlocal medium, Laser Phys. Lett. 2 (2005), 25-29, physics/0409139.
- Dreischuh A., Paulus G.G., Zacher F., Grasbon F.,
Walther H., Generation of multiple-charged optical vortex
solitons in a saturable nonlinear medium, Phys. Rev. E
60 (1999), 6111-6117.
- Suter D., Blasberg T., Stabilization of transverse
solitary waves by a nonlocal response of the nonlinear medium,
Phys. Rev. A 48 (1993), 4583-4587.
- Perez-Garcia V.M., Konotop V.V., Garcia-Ripoll J.J.,
Dynamics of quasicollapse in nonlinear Schrödinger systems with
nonlocal interactions, Phys. Rev. E 62 (2000), 4300-4308.
- Turitsyn S.K., Spatial dispersion of nonlinearity and stability of
multidimensional solitons, Teoret. Mat. Fiz. 64 (1985), 226-232
(English transl.: Theoret. and Math. Phys. 64 (1985), 797-801).
- Bang O., Krolikowski W., Wyller J., Rasmussen J.J., Collapse arrest and soliton stabilization in nonlocal nonlinear media, Phys. Rev. E 66 (2002), 046619, 5 pages, nlin.PS/0201036.
- Dreischuh A., Neshev D., Peterson D.E., Bang O., Krolikowski W.,
Observation of attraction between dark solitons, Phys.
Rev. Lett. 96 (2006), 043901, 4 pages, physics/0504003.
- Krolikowski W., Bang O., Rasmussen J.J., Wyller J., Modulational instability in nonlocal nonlinear
Kerr media, Phys. Rev. E 64 (2001), 016612, 8 pages, nlin.PS/0105049.
- Krolikowski W., Bang O., Nikolov N.I., Neshev D., Wyller J., Rasmussen J.J., Edmundson D., Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media, J. Opt. B Quantum Semiclass. Opt. 6 (2004), S288-S294,
nlin.PS/0402040.
- Roussignol P., Ricard D., Lukasik J., Flytzanis C., New results on optical phase conjugation in semiconductor-doped glasses, J. Opt. Soc. Amer. B Opt. Phys. 4 (1987), 5.
- Lederer F., Biehlig W., Bright solitons and light bullets in semiconductor waveguides, Electron. Lett. 30 (1994), 1871-1872.
- Lawrence B., Cha M., Torruellas W.E., Stegeman G.I., Etemad S., Baker G., Kajzar F., Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm, Appl. Phys. Lett. 64 (1994), 2773-2775.
- Doktorov E.V., Molchan M.A., Modulational instability in nonlocal Kerr-type
media with random parameters, Phys. Rev. A 75 (2007), 053819, 6 pages, arXiv:0704.1093.
- Wyller J., Krolikowski W., Bang O., Rasmussen J.J., Generic features of modulational instability in nonlocal Kerr media, Phys. Rev. E 66 (2002), 066615, 13 pages, nlin.PS/0105049.
- Novikov E.A., Functionals and the random force
method in turbulence theory, Zh. Exp. Teor. Fiz.
47 (1964), 1919-1926 (English transl.: Sov. Phys. JETP 20 (1964), 1290-1295).
|
|