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Grigorieva E. V., Kashchenko S. A. Normal and quasi-normal forms of the semiclassical laser equations with diffraction. Izvestiya VUZ. Applied Nonlinear Dynamics, 1995, vol. 3, iss. 1, pp. 59-72.

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Language: 
Russian
Heading: 
Autowaves. Self-organization
Article type: 
Article
UDC: 
517.946:621.373

Normal and quasi-normal forms of the semiclassical laser equations with diffraction

Autors: 
Grigorieva Elena Viktorovna, Belarus State Economic University (BSEU)
Kashchenko Sergej Aleksandrovich, P. G. Demidov Yaroslavl State University
Abstract: 

The transverse pattern formation of rotating and standing waves and transverse mode beating in laser are considered using of the normal form method. The complicated dynamics possibility due to the neutral stability solutions of the shortened equations is demonstrated.

Key words: 
-
Reference: 
  1. Lugiato LA. Spatio-temporal structures. Part 1. Phys. Rep. 1992;219(3-6):293-310. DOI: 10.1016/0370-1573(92)90144-O.
  2. Brambilla M , Battipede F, Lugiato LA, Penna V V, Prati F, Tamm C, Weiss CO. Transverse laser patterns. 1. Phase singularity crystals. Phys. Rev. A. 1991;43(9):5090-5113. DOI: 10.1103/physreva.43.5090.
  3. Jakobsen PK, Moloney JV, Newell AC, Indik R. Space-time dynamics of wide-gain-section lasers. Phys. Rev. A. 1992;45(11):8129-8137. DOI: 10.1103/physreva.45.8129.
  4. Staliunas K. Laser Ginzburg - Landau equation and laser hydrodynamics. Phys. Rev. A. 1993;48(2):1573-1581. DOI: 10.1103/physreva.48.1573.
  5. Collet Р, Gil L, Rocca F. Optical vortices. Opt. Commun. 1989;73:403-408. DOI: 10.1016/0030-4018(89)90180-6.
  6. Bruno АD. Local Methods in Nonlinear Differential Equations. Berlin: Springer; 1989. 348 p.
  7. Kashchenko SА. About quasi-normal forms for parabolic equations with low diffusion. Doklady Math. 1988;37(2):510-513.
  8. Kashchenko SА. Spatial features of high-mode bifurcations of two-component systems with low diffusion. Sov. J. Diff. Equat. 1989;25(2):193-199.
  9. Loper Ruiz R, Mindlin GB, Perez-Garcia C, Tredicce J. Mode-mode interaction for СО2 laser with imperfect O(2) symmetry. Phys. Rev. A 1993;47(1):500-509. DOI: 10.1103/physreva.47.500.
  10. Akhromeeva TS, Kurdyumov SP, Malinetskii GG, Samarskii АА. Classification of solutions of a system of nonlinear diffusion equations in a neighborhood of a bifurcation point. J. Math. Sci. 1988;41:1292-1356. DOI: 10.1007/BF01098786.
  11. Perez-Garcia VM, Guerra JM. Weak turbulent behavior and dynamical frequency locking in high-Fresnel-number laser. Phys. Rev. A. 1994;50(2):1646-1663. DOI: 10.1103/physreva.50.1646.
  12. Collet Р, Gil L, Lega J. А form of turbulence associated with defects. Physiса D. 1989;37(1-3):91-103. DOI: 10.1016/0167-2789(89)90119-X.
  13. Bekki N, Nozaki K. Formations of spatial patterns and holes in the generalized Ginzburg - Landau equation. Phys. Lett. A. 1985;110(3):133-135. DOI: 10.1016/0375-9601(85)90759-5.
  14. Grigorieva EV, Kashchenko SA. Complex temporal structures in models of a laser with optoelectronic delayed feedback. Opt. Commun. 1993;102(1-2):183-192. DOI: 10.1016/0030-4018(93)90489-R.
  15. Grigorieva EV, Kashchenko SA. Regular and chaotic pulsations in laser diode with delayed feedback. Int. J. Bif. Chaos. 1993;3(6):1515-1528. DOI: 10.1142/S0218127493001197.
  16. Arecchi FT, Giacomelli G, Ramazza PL, Residori S. Experimental evidance of chaotic itinerancy and spatio-temporal chaos in optics. Phys. Rev. Lett. 1990;65(20):2531-2534. DOI: 10.1103/PhysRevLett.65.2531.
  17. Ikeda K, Otsuka K, Matsumoro K. Maxwell - Bloch Turbulence. Progr. Theor. Phys. Suppl. 1989;99:295-324. DOI: 10.1143/PTPS.99.295.
  18. Otsuka K. Self-induced phase turbulence and chaotic itinerancy in coupled laser systems. Phys. Rev. Lett. 1990;65(3):329-332. DOI: 10.1103/PhysRevLett.65.329.
Received: 
14.10.1994
Accepted: 
14.02.1995
Published: 
15.09.1995
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