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2004 | 105 | 5 | 437-444
Article title

On Existence of Solitons for the 3rd Harmonic of a Light Beam in Planar Waveguides

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EN
Abstracts
EN
We consider equations governing propagation of a monochromatic laser beam coupled to its third harmonic in a nonlinear medium. The system proves to be non-integrable in the sense of Painleve. However it is partially integrable for all values of its parameters. We further check the possibility of solving the equations by the Hirota bilinear method. The system is found to be solvable this way provided that the complex phase of the third harmonics is equal to tripled phase of the fundamental mode (modulo i) and also the amplitudes of these modes are in special proportion. This result corresponds to the previously known condition of existence of the sech soliton solutions. Furthermore, the Hirota scheme is found to work only for exact resonance, i.e. for the ratio of the dispersion coefficients equal to the ratio of frequencies. Finally, all these conditions may only be satisfied for single envelope solitons of the cubic Schrödinger type.
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EN
Publisher

Year
Volume
105
Issue
5
Pages
437-444
Physical description
Dates
published
2004-05
received
2003-12-04
accepted
2004-04-26
Contributors
author
  • Institute of Physics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
author
  • The Andrzej Soltan Institute for Nuclear Studies, Hoża 69, 00-681 Warsaw, Poland
  • Institute of Experimental Physics, Optics Division, Warsaw University, Hoża 69, 00-681 Warsaw, Poland
References
  • 1. R.A. Sammut, A.V. Buryak, Y.S. Kivshar, J. Opt. Soc. Am. B 15, 1488 (1998)
  • 2. Yijiang Chen, Phys. Rev. A 50 5145 (1994)
  • 3. V. Cao Long, P.P. Goldstein, M. Trippenbach, D. Nguyen Tien, in: Proc. Nation. Conf. on Theoretical Physics, Sam Son (Vietnam), August 2003, in press
  • 4. R. Conte, in: The Painlevé Property One Century Later, Ed. R. Conte, Springer Verlag, New York 1999, ch. 3, p. 77; also M. Musette, ibidem, ch. 8, p. 517
  • 5. R. Hirota, Phys. Rev. Lett. 27, 1192 (1971); R. Hirota, in: Solitons, Eds. R.K. Bullough, P.J. Caudrey, Springer Verlag, Berlin 1980, p. 157
  • 6. J. Weiss, M. Tabor, G. Carnevale, J. Math. Phys. 24, 522 (1983); J. Weiss, J. Math. Phys. 25, 2226 (1984)
  • 7. M. Jimbo, M.D. Kruskal, T. Miwa, Phys. Lett. A 92, 59 (1982)
  • 8. J. Hietarinta, Int. J. Mod. Phys. A 12, 43 (1997); B. Grammaticos, A. Ramani, J. Hietarinta, Phys. Lett. A 190 65 (1994)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv105n503kz
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