V.A. Eremenko - Ph.D. (Phys.-Math.), Leading Research Scientist, Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Science (IZMIRAN)

E-mail: eremenko@izmiran.ru

N.I. Manaenkova - Ph.D. (Phys.-Math.), Senior Research Scientist, Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Science (IZMIRAN) E-mail: nat_man@mail.ru

The nonlinear problem of the wave propagation is considered. In addition to Kerr nonlinearity the question of the existence of concentrated solutions is analyzed for the threshold and saturable nonlinearity. It is shown that both in the case of threshold nonlinearity, and in the case of saturable nonlinearity solitary waves – concentrated solutions of the corresponding wave equations exist. In case of hybrid nonlinearity is taken into account influence simultaneously both processes of overcoming of threshold and saturation on interaction of the electromagnetic field and environment of the wave propagation. Concentrated solutions of the corresponding wave equations exist and are represented.

1. Ginzburg V.L., Gurevich A.V. Nelinejnye javlenija v plazme, proishodjashhie v peremennom jelektromagnitnom pole // Uspehi fizicheskih nauk. 1960. T. 70. S. 201–246.
2. Farley D.T. Artificial heating of the electrons in the F-region of the ionosphere //Journal of Geophysical Research. 1963. V. 68. P. 401–413.
3. Bochkarev G.S., Kim V.Ju., Lobachevskij L.A., Ljannoj B.E., Migulin V.V., Sergeenko O.S., Cherkashin Ju.N. Vzaimodejstvie dekametrovyh radiovoln na chastotah vblizi MPCh F2 pri naklonnom rasprostranenii //Geomagnetizm i Ajeronomija. 1979. T. 19. S. 830–833.
4. Bochkarev G.S., Eremenko V.A., Lobachevcky L.A., Ljannoy B.E., Migulin V.V., Cherkashin Yu.N. Non-linear interaction of decameter radio waves at close frequencies on oblique propagation //Journal of Atmospheric and Terrestrial Physics. 1982. V. 44. № 12. P. 1137–1141.
5. Bochkarev G.S., Eremenko V.A., Lobachevskij L.A., Ljannoj B.E., Migulin V.V., Cherkashin Ju.N. Modelirovanie vozdejstvija moshhnoj volny na ionosferu pri naklonnom padenii //Geomagnetizm i Ajeronomija. 1980. T. 20. S. 848–853.
6. Molotkov I.A., Cherkashin Yu.N. Some nonlinear effects of wave beams propagation in the ionosphere // Journal of Atmospheric and Terrestrial Physics. 1994. V. 56. № 11. P. 1477–1481.
7. Molotkov I.A. Analiticheskie metody v teorii nelinejnyh voln. M.: Fizmatlit. 2003.
8. Gatz Sand, Herrmann J. Soliton propagation in materials with saturable nonlinearity // J. Opt. Soc. Am. 1991. V. 8. № 11.
9. Eremenko V.A., Molotkov I.A. Osobennosti povedenija volnovyh puchkov v sredah s nasyshhajushhejsja nelinejnost'ju // Radiotehnika i jelektronika. 1998. T. 43. № 6. S. 657–660.
10. Molotkov I., Eremenko V., Anderson D., Lisak M. 2000 Stationary High Intensity Wave Beams in Media with Saturable Nonlinearity // Physica Scripta. 2000. V. 61. № 4. P. 472–475.