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Number of results
2004 | 106 | 6 | 843-852

Article title

On Existence of Solitons for the Second Harmonic Equations of a Laser Beam

Content

Title variants

Languages of publication

EN

Abstracts

EN
We look for conditions of existence of soliton solutions for equations governing propagation of a monochromatic laser beam coupled to its second harmonic in a nonlinear medium. The system proves to be non-integrable in the sense of Painlevé. However it is partially integrable for some 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 amplitudes of both modes are equal while the complex phase of the second harmonic is equal to the double phase of the fundamental mode (moduloπ). The Hirota scheme is found to work merely 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 by single envelope travelling waves, in which the envelope has locally the shape of the Weierstrass function.

Keywords

EN

Year

Volume

106

Issue

6

Pages

843-852

Physical description

Dates

published
2004-12
received
2004-08-17

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
author
  • Faculty of High Technology, Vinh University, Nghe An, Vietnam

References

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Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.bwnjournal-article-appv106n604kz
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