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One-dimensional waves in disperse nonlinear systems

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Literature Cited

  1. R. Courant and K. Friedrichs, Supersonic Flow and Shock Waves [Russian translation] Inost. Lit., Moscow (1950).

    Google Scholar 

  2. L. D. Landau and E. M. Lifshits, Mechanics of Continuous Media [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  3. D. J. Korteveg and G. de Vries, “Change in the shape of long waves advancing in a rectangular channel and a new type of long solitary waves, Phil. Mag.,39, 422, (1895).

    Google Scholar 

  4. G. Lamb, Hydrodynamics [Russian translation], Gostekhizdat, Moscow-Leningrad (1947).

    Google Scholar 

  5. L. N. Sretenskii, Theory of Wave Motions of Fluids [in Russian], ONTI, Moscow-Leningrad (1936).

    Google Scholar 

  6. A. I. Nekrasov, Exact Theory of Steady-State Waves on the Surface of a Heavy Fluid [in Russian], Izd. Akad. Nauk SSSR, Moscow (1951).

    Google Scholar 

  7. A. A. Andronov, A. A. Vitt, and S. É. Khaikin, Theory of Oscillations [in Russian], GIFML, Moscow (1959).

    Google Scholar 

  8. L. I. Mandel'shtam, Collected Works [in Russian], Vol. 4, Izd. Akad. Nauk SSSR, Moscow (1947).

    Google Scholar 

  9. N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], GIFML, Moscow (1958).

    Google Scholar 

  10. T. Hayashi, Nonlinear Oscillations in Physical Systems [Russian translation], Izd. Mir., Moscow (1968).

    Google Scholar 

  11. V. M. Fain and Ya. I. Khanin, Quantum Radio Physics [in Russian], Izd. Sov. Radio, Moscow (1965).

    Google Scholar 

  12. V. L. Ginzburg, Propagation of Electromagnetic Waves in a Plasma [in Russian], Izd. Nauka, Moscow (1967).

    Google Scholar 

  13. Y. R. Shen, “Electrostriction, optical Kerr effect, and self-focusing laser beams,” Phys. Lett.,20, No. 4, 378 (1966).

    Google Scholar 

  14. Ya. B. Zel'dovich and Yu. P. Raizer, Theory of Shock Waves and High-Temperature Hydrodynamic Phenomena [in Russian], Izd. Nauka, Moscow (1966).

    Google Scholar 

  15. V. I. Karpman, Nonlinear Waves in Dispersive Media (Lectures) [in Russian], Novosibirsk (1968).

  16. A. V. Gaponov, L. A. Ostrovskii, and G. I. Freidman, “Electromagnetic shock waves”, Izv. VUZ, Radiofiz.,10, Nos. 9–10, 1376 (1967).

    Google Scholar 

  17. S. A. Akhmanov and R. V. Khokhlov, Problems in Nonlinear Optics [in russian], Izd. Nauka, Moscow, (1964).

    Google Scholar 

  18. N. Bloembergen, Nonlinear Optics, [Russian translation], Izd. Mir, Moscow (1966).

    Google Scholar 

  19. S. A. Akhmanov, A. P. Sukhorukhov, and R. V. Khokhlov, “Self-focusing and light diffraction in a nonlinear medium,” Usp. Fiz. Nauk,93, No. 1, 19 (1967).

    Google Scholar 

  20. N. Bloembergen, “Stimulated Raman effect,” Amer. J. Phys.,35, 989 (1967).

    Google Scholar 

  21. V. I. Bespalov, A. G. Litvak, and V. I. Talanov, “Self-action of electromagnetic waves in cubic isotropic media,” Nonlinear Optics [in Russian], Izd. Nauka, Novosibirsk (1968).

    Google Scholar 

  22. P. K. Kryukov and V. S. Letokhov, “Propagation of light pulses in a resonant amplifying (absorbing) medium,” Usp. Fiz. Nauk,99, No. 2, 171 (1969).

    Google Scholar 

  23. V. N. Sytovich, Nonlinear Effects in a Plasma [in Russian], Izd. Nauka, Moscow (1966).

    Google Scholar 

  24. L. K. Zarembo and V. N. Krasil'nikov, Introduction to Nonlinear Acoustics, [in Russian], Izd. Nauk, Moscow (1966).

    Google Scholar 

  25. “Discussion of the nonlinear theory of wave propagation in dispersive systems (organized by N. J. Lighthill)”, Proc. Roy. Soc.,A209, No. 1456 (1967).

  26. Collection: The Theory of Surface Waves [Russian translation], Inost. Lit., Moscow (1959).

  27. W. H. Monk, “Solitary-wave theory and its application to surface problems,” N. Y. Acad. Sci. Ann.,51, No. 3, 376 (1949).

    Google Scholar 

  28. J. B. Keller, “The solitary wave and periodic waves in shallow water,” Comm. Pure Appl. Math.,1, 328 (1948).

    Google Scholar 

  29. G. D. Capper, “An exact solution for progressive capillary waves of arbitrary amplitude,” J. Fluid Mech.,2, 232 (1967).

    Google Scholar 

  30. A. A. Vedenov, E. P. Velikhov, and R. Z. Sagdeev, “Nonlinear Oscillations of Rarefied Plasma. I,” Nuclear Synthesis [in Russian], Vol. 1 (1961), p. 82.

    Google Scholar 

  31. R. Z. Sagdeev, “Collective processes and shock waves in rarefied plasma,” Problems of Plasma Theory [in Russian], No. 4, Atomizdat (1964), p. 20.

    Google Scholar 

  32. Yu. F. Filippov, The theory of propagation of stationary finite-amplitude waves in ferrites,” Izv. Vuz, Radiofiz,8, No. 2, 292 (1965).

    Google Scholar 

  33. S. M. Fainshtein, “Nonlinear waves in a stream—plasma system,” Izv. VUZ, Radiofiz.,10, No. 8, 1110 (1967).

    Google Scholar 

  34. T. Z. Sokhov and L. N. Gurman, Mesometeorological solitary waves,” Izv. Akad. Nauk SSSR, Fiz. Atmosfery i Okeana,4, No. 3, 271 (1968).

    Google Scholar 

  35. V. T. Gurovich and V. I. Karman, “Dynamics of electroacoustic waves in liquid and plasma,” Zh. Éksperim. i Teor. Fiz.,56, No. 6, 1952 (1969).

    Google Scholar 

  36. A. Jeffrey and T. Taniuti, Propagation of Nonlinear Waves, Academic, New York (1964).

    Google Scholar 

  37. A. G. Kulikovskii and G. A. Lyubimov, Magnetohydrodynamics [in Russian], GIFML, Moscow (1968).

    Google Scholar 

  38. E. Anderson, Shock Waves in Magnetohydrodynamics [in Russian], Atomizdat, Moscow (1968).

    Google Scholar 

  39. R. V. Polovin, “Nonlinear magnetohydrodynamic waves”, Differents. Uravn.,1, No. 4, 499 (1965).

    Google Scholar 

  40. R. Z. Sagdeev, “Fine structure of a shock wave front propagating across the magnetic field in rarefied plasma,” Zh. Tekh. Fiz.,31, 1955 (1961).

    Google Scholar 

  41. S. M. Fainshtein, “Stationary waves in plasma containing an electric field,” Izv. VUZ, Radiofiz.,11, No. 9, 1300 (1968).

    Google Scholar 

  42. A. M. Belyantsev, Yu. K. Bogatyrev, A. V. Gaponov, E. Ya. Daume, L. A. Ostrovskii, L. I. Solov'eva, and G. I. Freidman, Electromagnetic Waves in Transmission Lines Having Nonlinear Parameters, URSI, Proc. of the Fourteenth General Assembly, XIII-6 (1953), p. 251.

  43. I. G. Kataev, Electromagnetic Shock Waves [in Russian], Izd. Sov. Radio, Moscow (1963).

    Google Scholar 

  44. M. I. Rabinovich, “Self-oscillations in a ring line with distributed nonlinear parameters,” Izv. VUZ, Radiofiz.,8, No. 4, 795 (1965).

    Google Scholar 

  45. A. V. Gaponov, L. A. Ostrovskii, and M. I. Rabinovich, “Electromagnetic waves in nonlinear transmission lines with active parameters,” Electromagnetic Wave Theory (J. Brown, ed.), Pergamon (1967), p. 587.

  46. M. I. Rabinovich, “Effect of dispersion on self-oscillations in a nonlinear active line,” Izv. VUZ, Radiofiz.,9, No. 1, 173 (1966).

    Google Scholar 

  47. M. I. Rabinovich, “Self-oscillations in a transmission line with tunnel diodes,” Radiotekhnika i Élektronika,11, No. 8, 1467 (1966).

    Google Scholar 

  48. Yu. K. Bogatyrev and M. I. Rabinovich, “Investigation of self-oscillations in an active ring line,” Izv. VUZ, Radiofiz.10, No. 1, 128 (1967).

    Google Scholar 

  49. S. M. Fainshtein, “Steady-state oscillations in a stream—plasma system,” Izv. VUZ, Radiofiz.,11, No. 6, 834 (1968).

    Google Scholar 

  50. S. M. Fainshtein, “Stationary ion-sound waves in a stream—plasma system,” Izv. VUZ, Radiofiz.,12, No. 4, 547 (1969).

    Google Scholar 

  51. Yu. L. Klimontovich, P. S. Landa, and E. G. Lariontsev, “Stability of the oppositely traveling wave mode in a ring gas laser,” Zh. Éksperim. i Teor. Fiz.,52, No. 6, 1616 (1967).

    Google Scholar 

  52. S. G. Zeiger and É. E. Fradkin, “Competition between two oscillation modes in a traveling-wave laser,” Opt. i Spektr., 21, No. 3, 386 (1965).

    Google Scholar 

  53. E. M. Belinov and A. N. Oraevskii, “Radiation regimes of a gas laser having a ring cavity resonator,” Dokl. Akad. Nauk SSSR,180, No. 1, 56 (1968).

    Google Scholar 

  54. T. M. Il'inova and R. V. Khokhlov, “Wave processes in lines with shunting-wave impedance,” Radiotekhnika i Élektronika,8, No. 12, 2006 (1963).

    Google Scholar 

  55. Yu. I. Vorontsov, “Propagation velocity of stationary signals in transmission lines having a nonlinear resistance,” Radiotekhnika i Élektronika,9, No. 9, 1709 (1964).

    Google Scholar 

  56. Yu. K. Bogatyrev and L. A. Ostrovskii, “Propagation of electromagnetic waves in nonlinear transmission lines with lumped parameters. I and II,” Izv. VUZ, Radiofiz.,6, No. 5, 973, 985 (1963).

    Google Scholar 

  57. N. J. Zabusky and M. D. Kruskal, “Interaction of ‘solitons’ and a collisionless plasma and the recurrence of initial states,” Phys. Rev. Lett.,15, No. 6, 240 (1965).

    Google Scholar 

  58. Yu. A. Berezin and V. I. Karpman, Nonlinear evolution of perturbations in plasma and other dispersive media,” Zh. Éksperim i Teor. Fiz.,51, No. 5 (11), 1556 (1966).

    Google Scholar 

  59. Yu. K. Bogatyrev, “Nonlinear theory of a distributed amplifier based on tunnel diodes,” Izv. VUZ, Radiofiz. (in press).

  60. V. L. Ginzburg and A. V. Gurevich, “Nonlinear phenomena in plasma, occuring in an alternating electromagnetic field,” Usp. Fiz. Nauk,70, No. 2, 201 (1960).

    Google Scholar 

  61. L. A. Ostrovskii, “Propagation of wave packets and space—time self-focusing in a nonlinear medium,” Zh. Éksperim. i Teor. Fiz.,51, No. 4, (10), 1189 (1966).

    Google Scholar 

  62. F. de Martini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening light pulses,” Phys. Rev.,164, No. 2, 312 (1967).

    Google Scholar 

  63. L. A. Ostrovskii, “Frequency spectrum of self-focusing of light pulses,” Pis'ma v Zh. Éksperim. i Teor. Fiz.,6, No. 8, 807 (1967).

    Google Scholar 

  64. F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett.,19, No. 19, 1097 (1967).

    Google Scholar 

  65. L. A. Ostrovskii, “Frequency modulation and expansion of the spectrum of optical pulses in nonlinear media,” Transactions of the First Vavilov Conference on Nonlinear Optics [in Russian], Izd. Nauka, Novosibirsk (1969).

    Google Scholar 

  66. J. E. Feir, “Some results from wave-pulse experiments,” Proc. Roy. Soc.,A 299, 54 (1967).

    Google Scholar 

  67. V. M. Ovchinnikov and V. E. Khartsiev, “Bleaching waves in two-level systems,” Zh. Éksperim. i Teor. Fiz.,49, No. 1 (7), 315 (1965).

    Google Scholar 

  68. V. I. Talanov, “Propagation of short electromagnetic pulses in active media,” Izv. VUZ, Radiofiz.,7, No. 3, 491 (1964).

    Google Scholar 

  69. T. M. Il'inova and R. V. Khokhlov, “Nonlinear properties of the laser as an amplifier,” Izv. VUZ, Radiofiz.,8, No. 5, 899 (1965).

    Google Scholar 

  70. Ya. I. Frenkel', Collected Works [in Russian], Vol. 3, Izd. Akad. Nauk SSSR, Moscow (1959).

    Google Scholar 

  71. M. J. Lighthill, “Contribution to the theory of waves in nonlinear dispersive systems,” J. Inst. Math. Appl.,1, 269 (1965).

    Google Scholar 

  72. L. A. Ostrovskii, “Nonstationary wave processes in nonlinear dispersive media,” Nonlinear Optics [in Russian], Nauka, Novosibirsk (1958).

    Google Scholar 

  73. M. J. Lighthill, “Some special cases treated by the Whitham theory,” Proc. Roy. Soc.,A, 299, 28 (1967).

    Google Scholar 

  74. L. A. Ostrovskii, “Propagation of frequency-modulated signals in dispersive systems,” Radiotekhnika i Élektronika,10, No. 7, 1176 (1965).

    Google Scholar 

  75. L. A. Ostrovskii, “Electromagnetic waves in nonlinear media having dispersion,” Zh. Tekh. Fiz.,33, No. 8, 905 (1963).

    Google Scholar 

  76. L. A. Ostrovskii, “Propagation of modulated waves in nonlinear dispersive media,” Electromagnetic Wave Theory (J. Brown, ed.), Pergamon (1967), p. 581.

  77. T. Benjamin, “Instability of periodic wave trains in nonlinear dispersive systems,” Proc. Roy. Soc.,A299, 59 (1967).

    Google Scholar 

  78. T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along magnetic field in cold plasma,” Phys. Rev. Letters,21, 209 (1968).

    Google Scholar 

  79. V. I. Karpman, “Self-modulation of nonlinear plane waves in dispersive media,” Pis'ma v Zh. Éksperim. i Teor. Fiz.,6, No. 8, 829 (1967).

    Google Scholar 

  80. L. A. Ostrovskii, “Shock envelope waves,” Zh. Éksperim. i Teor. Fiz.,54, No. 4, 1235 (1968).

    Google Scholar 

  81. T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lefshitz, and P. L. Kelley, “Self-modulation, self-steepening, and spectral development of light in small-scale trapped filaments,” Phys. Rev., 177, No. 3, 305 (1969).

    Google Scholar 

  82. A. G. Litvak and V. I. Talanov, “Application of a parabolic equation for the calculation of fields in dispersive nonlinear media,” Izv. VUZ, Radiofiz.,10, No. 4, 539 (1967).

    Google Scholar 

  83. V. V. Zakharov, “On the instability of self-focusing of light,” Zh. Éksperim. i Teor. Fiz.,53, 735 (1967).

    Google Scholar 

  84. M. I. Rabinovich, “Interaction of wave packets in an active medium,” Abstract of Papers Presented at the Fourth All-Union Conference on Nonlinear Optics [in Russian], Izd. Mos. Gos. Un-ta, Moscow (1968).

    Google Scholar 

  85. L. I. Zagryadskaya and L. A. Ostrovskii, “Observations of self-action of modulated waves in a nonlinear line,” Izv. VUZ, Radiofiz.,11, No. 6, 948 (1968).

    Google Scholar 

  86. L. A. Ostrovskii, “Theory of ‘envelope waves’ in nonlinear dispersive media,” URSI Symposium on Electromagnetic Waves (Selected Papers); Alta Frequenza,38, N. Special,4–4, 207 (1967).

  87. G. B. Whitham, “General approach to linear and nonlinear dispersive waves using a Lagrangian,” J. Fluid. Mech.,22, No. 2, 273 (1965).

    Google Scholar 

  88. E. B. Whitham, “Nonlinear dispersion of water waves,” J. Fluid. Mech.,27, No. 2, 399 (1967).

    Google Scholar 

  89. G. B. Whitham, “Variational methods and applications to water waves,” Proc. Roy. Soc.,A,299, No. 6 (1967).

  90. E. N. Pelinovskii, Application of the Hamilton Principle in Averaged Form to the Process of Nonlinear Waves [in Russian], Doctoral Thesis, Gor'kii State University (1969).

  91. L. A. Ostrovskii and E. N. Pelinovskii, “Transformation of waves on the surface of a liquid of variable depth,” Izv. Akad. Nauk SSSR, Fiz. Atmosfery i Okeana (in press).

  92. J. C. Luke, “Perturoation method for nonlinear dispersive-wave problems,” Proc. Roy. Soc.,A 292, 403 (1966).

    Google Scholar 

  93. M. I. Rabinovich, “Method of averaging over stationary waves,” Izv. VUZ, Radiofiz.,10, No. 2, 214 (1967).

    Google Scholar 

  94. P. D. Lax, “Integrals of nonlinear equations of evolution and solitary waves,” Comm. Pure Appl. Math.,21, 467 (1968).

    Google Scholar 

  95. R. V. Khokhlov, “Propagation of waves in nonlinear dispersive lines,” Radiotekhnika i Élektronika,6, No. 7, 1116 (1961).

    Google Scholar 

  96. V. I. Bespalov, V. M. Kubarev, and G. A. Pasmanik, “Stimulated Rayleigh scattering of light,” Izv. VUZ, Radiofiz. (in press).

  97. S. A. Akhmanov, V. G. Dmitriev, V. P. Modenov, and V. V. Fadeev, “Theory of parametric oscillations in a resonator filled with a nonlinear medium,” Radiotekhnika i Élektronika,19, No. 12, 2157 (1965).

    Google Scholar 

  98. M. I. Rabinovich and S. M. Fainshtein, “Generation of longitudinal waves at combinational frequencies in a stream—plasma system,” Zh. Éksperim. i Teor. Fiz.,57, No. 4 (10), 1308 (1969).

    Google Scholar 

  99. M. I. Rabinovich and S. M. Fainshtein, “Self-oscillatory processes in a stream—plasma system”, Transactions of the Fifth International Conference on Nonlinear Oscillation, 1969 [in Russian], Izd. Naukova Dumka, Kiev (in press).

  100. B. P. Kirsanov, “Nonlinear interactions of electromagnetic waves in an active medium and the possibility of their use to create new types of lasers,” Tr. FIAN,43, 187 (1968).

    Google Scholar 

  101. G. L. Gurevich and Yu. G. Khronopulo, “Problem of resonance parametric interaction of powerful fields at optical frequencies,” Zh. Éksperim, i Teor. Fiz.,51, No. 11, 1499 (1966).

    Google Scholar 

  102. W. Lewisell, Coupled and Parametric Oscillations in Electronics [Russian translation], Inost, Lit., Moscow (1963).

    Google Scholar 

  103. M. I. Rabinovich, On the Averaging Methods in Nonlinear Optics, Transactions of the First Vavilov Conference on Nonlinear Optics [in Russian], Izd. Nauka, Novosibirsk (1969).

    Google Scholar 

  104. V. N. Oraevskii and R. Z. Sagdeev, “On the stability of steady-state longitudinal plasma oscillations,” Zh. Tekh. Fiz.,32, 1291 (1962). Dokl. Akad. Nauk SSSR,147, 71 (1962).

    Google Scholar 

  105. V. E. Zakharov, “Stability of waves in disperse nonlinear media,” Zh. Éksperim. i Teor. Fiz.,51, No. 4 (10), 1107 (1966).

    Google Scholar 

  106. R. h. Enns and I. P. Batra, “Saturation and depletion in stimulated light scattering,” Phys. Lett.,28A, No. 8, 591 (1969).

    Google Scholar 

  107. V. T. Platonenko and R. V. Khokhlov, “Mechanism of operation of a combinational laser,” Zh. Éksperim. i Teor. Fiz.,46, No. 2, 555 (1964).

    Google Scholar 

  108. M. I. Rabinovich and E. I. Yakubovich, “Application of the averaging method to an investigation of distributed systems with a small nonlinearity,” Izv. VUZ, Radiofiz.,9, No. 5, 987 (1966).

    Google Scholar 

  109. M. I. Rabinovich, Self-oscillations of Distributed Active Systems, Dissertation, Gor'kii State University (1967).

  110. M. I. Rabinovich and S. M. Fainshtein, “Self-oscillations in a two-stream plasma with coulomb particle collisions. Excitation of electromagnetic waves in a stream—plasma system with coulomb friction,” Zh. Tekh. Fiz. (in press).

  111. W. E. Lamb, “Theory of optical masers,” Phys. Rev.,134, 1429 (1964).

    Google Scholar 

  112. S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, “Nonstationary phenomena and the space—time analogy in nonlinear optics,” Zh. Éksperim. i Teor. Fiz.,55, No. 4(10) 1430 (1968).

    Google Scholar 

  113. M. M. Sushchik, V. M. Fortus, and G. I. Freidman, “Imprisonment' of parametrically coupled waves by pulses and beams of pumping radiation,” Izv. VUZ, Radiofiz.,12, No. 2, 293 (1969).

    Google Scholar 

  114. M. M. Sushchik, V. M. Fortus, and G. I. Freidman, “Parametric amplification and generation of light,” Izv. VUZ, Radiofiz. (in press).

  115. L. A. Ostrovskii, “Interaction of wave packets in a nonlinear medium,” Izv. VUZ, Radiofiz.,12, No. 2, 268 (1969).

    Google Scholar 

  116. G. L. Gurevich and Yu. A. Otmakhov “Nonstationary processes during Stokes transformation,” Radiotekhnika i Élecktronika,”11, No. 12, 2226 (1966).

    Google Scholar 

  117. C. Gardner, J. Greene, M. Kruskal, and R. Miura, “A method for solving the Korteveg—de Vries equation,” Phys. Rev. Lett.,19, 1095 (1967).

    Google Scholar 

  118. L. A. Ostrovskii, “Interaction of electromagnetic shock waves in nonlinear transmission lines,” Izv. VUZ, Radiofiz.,8, No. 2, 285 (1965).

    Google Scholar 

  119. G. M. Zaslavskii and N. N. Filonenko, “Kinetics of nonlinear waves in a medium having dispersion,” Zh. Éksperim. i Teor. Fiz.,57, No. 4(10), 1240 (1969).

    Google Scholar 

  120. Ya. G. Panovko and I. I. Gubanova, Stability and Oscillations of Elastic Systems [in Russian], Izd. Nauka, Moscow (1964).

    Google Scholar 

  121. Yu. A. Mitropol'skii, Problems in the Asymptotic Theory of Nonstationary Oscillations [in Russian], Izd. Nauka, Moscow (1964).

    Google Scholar 

  122. Yu. A. Mitropolskii and B. I. Moseenkov, Lectures on the Application of Asymptotic Methods to the Solution of Partial Differential Equations [in Russian], Izd. AN USSR, Kiev (1968).

    Google Scholar 

  123. G. Caudereo, Nonlinear Mechanics [Russian translation], Inost. Lit., Moscow (1961).

    Google Scholar 

  124. B. I. Moseenkov, “Investigation of one-frequency oscillations and mechanical systems described by one-dimensional boundary-value problems with linear boundary conditions,” Transactions of the Fifth International Conference on Nonlinear Oscillations, 1969 [in Russian], Naukova Dumka, Kiev (in press).

    Google Scholar 

  125. L. A. Ostrovskii and E. I. Yakubovich, “Averaged laser equations and their stationary solutions,” Zh. Éksperim. i Teor Fiz.,46, No. 3, 963 (1964).

    Google Scholar 

  126. L. A. Ostrovskii and E. I. Yakubovich, “Steady-state oscillations of a laser having distributed losses,” Izv. VUZ, Radiofiz.,8, No. 1, 91 (1965).

    Google Scholar 

  127. T. I. Kuznetsova and S. G. Rautian, “Planar solutions of the wave equation for a layer having a negative absorption coefficient when saturation is considered,” Izv. VUZ, Radiofiz,7, No. 4, 682 (1964).

    Google Scholar 

  128. V. S. Kovalenko, “Theory of continuous-wave oscillations in a laser with allowance for diffusion effects,” Izv. VUZ, Radiofiz.,10, No. 2, 197 (1967).

    Google Scholar 

  129. Yu. K. Bogatyrev and M. I. Rabinovich, “Self-oscillations in a section of nonlinear active line,” Izv. VUZ, Radiofiz.,10, No. 12, 1750 (1967).

    Google Scholar 

  130. E. I. Yakubovich, “General properties of the average polarizabilities in nonlinear quasioptics,” Zh. Éksperim. i Teor. Fiz.,56, No. 2, 676 (1969).

    Google Scholar 

  131. T. I. Kuznetsova, “Interaction of electromagnetic fields with active media,” Tr. FIAN,43, 116 (1968).

    Google Scholar 

  132. H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys.,39, No. 10, 4662 (1968).

    Google Scholar 

  133. N. D. Milovskii, “Stability of a regenerative traveling-wave laser,” Izv. VUZ, Radiofiz. (in press).

  134. B. I. Bespalov and G. A. Pasmanik, “Stimulated Mandel'shtam—Brillouin back-scattering and stimulated entropy back-scattering of light pulses,” Zh. Éksperim. i Teor. Fiz. (in press).

  135. V. I. Bespalov and É. Ya. Daum, “Limiting parameters of ultrashort laser radiation pulses for resonant modulation of the losses,” Zh. Éksperim. i Teor. Fiz.,55, No. 4 (10), 1321 (1968).

    Google Scholar 

  136. T. I. Kuznetsova, “Narrowing of light pulses in a system with a bleaching filter,” Abstracts of Papers Read at the Fourth All-Union Conference on Nonlinear Optics [in Russian], Izd. Mos. Gos. Univ., Moscow (1968).

    Google Scholar 

  137. G. L. Gurevich and Yu. A. Otmakhov, “Nonstationary processes in a traveling-wave laser with a bleaching filter,” Izv. VUZ, Radiofiz.,12, No. 2, 208 (1969).

    Google Scholar 

  138. G. L. Gurevich, “Theory of traveling wave oscillators in the optical range,” Izv. VUZ, Radiofiz., (in press).

  139. V. M. Pashkin, Effect of Inhomogeneities on the Character of Nonlinear Interactions in a One-Dimensional Self-oscillatory System [in Russian], Doctoral Thesis, Gor'kii State University (1969).

  140. A. E. Siegman, “Nonlinear optical effects and optical power limits,” Appl. Optics,1, No. 6, 739 (1962).

    Google Scholar 

  141. A. E. Kaplan, Yu. A. Kravtsov, and V. A. Rylov, Parametric Oscillators and Frequency Dividers [in Russian], Izd. Sov. Radio, Moscow (1966).

    Google Scholar 

  142. P. K. Tien and H. Suhl, “A traveling-wave ferromagnetic amplifier,” Proc. IRE,46, No. 4 (1968).

  143. S. A. Akhmanov and R. V. Khokhlov, “Trigger properties of nonlinear waveguide systems,” IzV. VUZ, Radiofiz.,5, No. 4, 742 (1962).

    Google Scholar 

  144. A. I. Vesnitskii, L. A. Ostrovskii, V. V. Papko, and V. N. Shabanov, “Pulsed parametric oscillations in in distributed systems,” Pis'ma v Zh. Éksperim. i Teor. Fiz.,9, No. 5, 274 (1969).

    Google Scholar 

  145. B. V. Chirikov, Investigations in Linear Resonance and Stochasticity Dissertation, Institute of Nuclear Physics, Novosibirsk (1969); Atom. Énerg.,6, 630 (1969).

    Google Scholar 

  146. M. I. Rabinovich, “Asymptotic method in the theory of nonlinear oscillations of distributed systems,” Dokl. Akad. Nauk SSSR (in press).

  147. A. V. Gaponov, L. A. Ostrovskii, and M. I. Rabinovich, “Asymptotic methods in nonlinear theory of oscillations of distributed systems,” Transactions of the Fifth International Conference on Nonlinear Oscillations, 1969 [in Russian], Izd. Naukova Dumka, Kiev (in press).

    Google Scholar 

  148. T. Taniuti and N. Yajima, “A perturbation method for nonlinear wave modulation. I,” J. Math. Phys.,10, No. 8, 1369 (1969).

    Google Scholar 

  149. V. I. Karpman and E. M. Kruskal, “Modulated waves in nonlinear dispersive media,” Zh. Éksperim. i Teor. Fiz.,55, No. 2, 530 (1968).

    Google Scholar 

  150. G. I. Freidman, A. V. Gaponov, L. A. Ostrovskii, and M. I. Rabinovich, Proc. Roy. Soc.,A 312, 395 (1969).

    Google Scholar 

  151. G. M. Zaslavskii, “Kinetic equation for a gas with solitons,” Pis'ma v Zh. Éksperim. i Teor. Fiz.,9, No. 12, 689 (1969).

    Google Scholar 

  152. N. N. Filonenko, “Evolution of a nonlinear periodic wave in the presence of resonant perturbations,” Izv. VUZ, Radiofiz. (in press).

  153. V. E. Zakharov, “Dissipative instabilities of a light wave in nonlinear dielectrics,”. Pis'ma v Zh. Éksperim. i Teor. Fiz.,7, No. 8, 290 (1968).

    Google Scholar 

  154. E. S. Cassidy, The Parametric Coupling Modes of Propagation in Nonlinear Media, Electromagnetic Wave Theory (J. Brown, ed.), Part 2 (1967), p. 543.

  155. V. M. Fortus and G. I. Freidman, On Selflocking of Modes in Parametric Light Oscillators, Izv. VUZ, Radiofiz.,12, No. 12, 1788 (1969).

    Google Scholar 

  156. V. I. Bespalov and G. I. Freidman, “Spectral and optical characteristics of giant pulses,” Izv. VUZ, Radiofiz.,9, No. 3, 513 (1966).

    Google Scholar 

  157. J. Comly and E. Garmire, “Second-harmonic generation from short pulses,” Appl. Phys.,12, No. 7 (1968).

  158. S. L. Shapiro, “Second-harmonic generation in LiNbO3 by picosecond pulses,” Appl. Phys. Lett.,13, No. 1, 19 (1968).

    Google Scholar 

  159. W. H. Glen, “Parametric amplification of ultrashort laser pulses,” Appl. Phys. Lett.,11, No. 11, 333 (1967).

    Google Scholar 

  160. S. G. Zeiger, “Effect of longitudinal dimensions on an active medium on the generation of axial laser modes,” Zh. Tekh. Fiz.38, 68 (1968).

    Google Scholar 

  161. W. Chester and J. A. Bones, “Resonant interaction of water waves. I, II,” Proc. Roy. Soc.A 306, No. 1484, 5, 23 (1968).

    Google Scholar 

  162. Ya. I. Khanin, “Effect of resonator-field inhomogeneity on transients in a laser” Izv. VUZ, Radiofiz.,12, No. 2, 202 (1969).

    Google Scholar 

  163. V. N. Genkin and P. M. Mednis, “Problem of frequency multiplication using semiconductors in the microwave range,” Izv. VUZ, Radiofiz.,11, No. 4, 611 (1968).

    Google Scholar 

  164. A. M. Belyantsev and V. N. Genkin, “Linear receiver for the submillimeter range,” Izv. VUZ, Radiofiz.,12, No. 5, 763 (1969).

    Google Scholar 

  165. A. M. Belyantsev, V. N. Genkin, V. A. Kozlov, and V. I. Piskarev, “Contribution of the nonparabolicity of the bands to the nonlinear susceptibility of InSb,” Pis'ma v Zh. Éksperim. i Teor. Fiz. (in press).

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Authors
  1. A. V. Gaponov
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  2. L. A. Ostrovskii
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  3. M. I. Rabinovich
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Additional information

This paper is the first of a series of review papers on practical problems in radio physics which will be published in our journal during the year. — The Editors.

Scientific-Research Radiophysical Institute, Gor'kii University. Translated from Izvestiya VUZ, Radiofizika, Vol. 13, No. 2, pp. 164–213, February, 1970.

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Gaponov, A.V., Ostrovskii, L.A. & Rabinovich, M.I. One-dimensional waves in disperse nonlinear systems. Radiophys Quantum Electron 13, 121–161 (1970). https://doi.org/10.1007/BF01031524

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