Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T03:15:14.219Z Has data issue: false hasContentIssue false
  • English
  • Français

Soliton emission in the forced non-linear Schrödinger equation

Published online by Cambridge University Press:  09 March 2009

O. Larroche ,
M. Casanova ,
D. Pesme  and
M. N. Bussac
O. Larroche
Affiliation:
CEA-CELV B.P.27 94190 Villeneuve St Georges, France
M. Casanova
Affiliation:
CEA-CELV B.P.27 94190 Villeneuve St Georges, France
D. Pesme
Affiliation:
CPT, Ecole Polytechnique, 91128 Palaiseau Cedex, France
M. N. Bussac
Affiliation:
CPT, Ecole Polytechnique, 91128 Palaiseau Cedex, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The plasma waves generated by resonant absorption of light in the vicinity of the critical density of laser-produced plasmas, are modelled by a non-linear Schrödinger equation with additional terms accounting for the presence of a source and the inhomogeneity of the medium.

We use an average lagrangian method to describe the behaviour of the solutions of this equation in the range of parameters where periodic soliton generation occurs. An iterating scheme describing the successive emission of solitons yields values for this range of parameters which are in reasonable agreement with those found from direct numerical simulations of the non-linear Schrödinger equation.

Type
Research Article
Information
Laser and Particle Beams , Volume 4 , Issue 3-4 , August 1986 , pp. 545 - 553
Copyright
Copyright © Cambridge University Press 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ablowitz, M. J. & Segur, H. 1981 “Solitons and the Inverse Scattering Transform”, SIAM Studies in Applied Mathematics 4.CrossRefGoogle Scholar
Adam, J. C., Gourdin-Serveniere, A. & Laval, G. 1982 Phys. Fluids, 25, 376.CrossRefGoogle Scholar
Anderson, D. 1983 Phys. Rev. A27, 3135.CrossRefGoogle Scholar
Anderson, D., Bondeson, A., & Lisak, M. 1979 J. Plasma Phys. 22, 339.CrossRefGoogle Scholar
Briand, J., El Tamer, M., Adrian, V., Gomes, A., Quemener, Y., Kieffer, J. C., & Dinguirard, J. P. 1984 Phys. Fluids, 27, 2588.CrossRefGoogle Scholar
Bussac, M. N., Lochak, P., Meunier, C. & Heron-Gourdin, A. 1985 Physica, 17D, 313.Google Scholar
Chen, H. H. & Liu, C. S. 1976 Phys. Rev. Lett. 37, 693.CrossRefGoogle Scholar
Chen, H. H. & Liu, C. S. 1978 Phys. Fluids, 21, 377.CrossRefGoogle Scholar
Cheung, P. Y. & Wong, A. Y. 1985 Phys. Rev. Lett. 55, 1880.CrossRefGoogle Scholar
Galeev, A. A., Sagdeev, R. Z., Sigov, Yu. S., Shapiro, V. D. & Shevchenko, V. I. 1975 Sov. J. Plasma Phys. 1, 5.Google Scholar
Goldman, M. V. 1984 Rev. Mod. Phys. 56, 709.CrossRefGoogle Scholar
Gourdin Serveniere-Heron, A. & Adam, J. C. 1984 Phys. Fluids, 27, 2005.CrossRefGoogle Scholar
Hasegawa, A. 1970 Phys. Rev. A1, 1746.CrossRefGoogle Scholar
Hirota, R. 1973 J. Math. Phys. 14, 805.CrossRefGoogle Scholar
Karpman, V. I. & Solovev, V. V. 1981 Physica, 3D, 487.Google Scholar
Kim, H. C., Stenzel, R. L. & Wong, A. Y. 1974 Phys. Rev. Lett. 33, 886.CrossRefGoogle Scholar
Laedke, E. W. & Spatschek, K. H. 1980 Phys. Rev. Lett. 45, 993.CrossRefGoogle Scholar
Morales, G. J. & Lee, Y. C. 1974 Phys. Rev. Lett. 33, 1016.CrossRefGoogle Scholar
Morales, G. J. & Lee, Y. C. 1977 Phys. Fluids, 20, 1135.CrossRefGoogle Scholar
Morisson, P. J., Meiss, J. D. & Cary, J. R. 1984 Physica, 11D, 324.Google Scholar
Satsuma, J. & Yajima, N. 1974 Suppl. Prog. Theor. Phys. 55, 284.CrossRefGoogle Scholar
Shukla, P. K. & Spatschek, K. H. 1978 J. Plasma Phys. 19, 387.CrossRefGoogle Scholar
Zakharov, V. E. 1972 Sov. Phys. JETP, 35, 908.Google Scholar
Zakharov, V. E. & Shabat, A. B. 1972 Sov. Phys. JETP, 34, 62.Google Scholar