Abstract
We shall analyze the oscillation and wave phenomena, and their corresponding models, in nonlinear systems and media (i.e., nonlinear oscillations and nonlinear waves) in parallel, as we did in the first part of the book. We have a few short remarks to make, mainly historical.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A.V. Gaponov-Grekhov and M.I. Rabinovich, “L.I. Mandel’shtam and the modern theory of nonlinear oscillations,” UFN, 128, 579–624 (1979).
L.I. Mandel’shtam, Lectures on Oscillation Theory [in Russian], Nauka, Moscow (1972).
A. Blaquiere, Nonlinear Systems Analysis [Russian translation], Mir, Moscow (1969).
V.L. Bratman, N.S. Ginzburg, and M.I. Petelin, “Theory of free electron lasers and masers” in: Lectures on Microwave Electronics and Radiophysics, 5-th Summer School-Seminar for Engineers [in Russian], Izd. Saratovskogo Univ., Saratov (1981), Vol.4, pp. 69–172.
A.V. Gaponov, M.I. Petelin, and V.K. Yulpatov, “Induced radiation of excited classical oscillators and its application to microwave electronics,” Izv. Vuzov: Radiotekh., 10, 1414–1453 (1967).
B.B. Kadomtsev, Group Phenomena in Plasmas [in Russian], Nauka, Moscow (1976).
L.A. Vainstein, “Electron waves in breaking systems. On the nonlinear equations of the travelling wave tube,”“Radio i Elekt., 2, 688–695 (1957).
L.A. Vainstein, “Nonlinear theory of travelling wave tubes,” Radio i Elekt., 2, 883–894 (1957).
L.A. Vainstein, “Nonlinear theory of travelling wave tubes,” Radio i Elekt., 2, 1027–1047 (1957).
V.T. Ovcharov (ed), Travelling Wave Tube, Collection of Translated Articles [Russian translation], Gosenergoizdat, Moscow (1959).
G.M. Zaslavskii and B.V. Chirikov, “Stochastic Instability of nonlinear oscillations,” UFN, 105, 7–13 (1971).
L.D. Landau and E.M. Lifshits, Mechanics [in Russian], Nauka, Moscow (1965).
G.M. Zaslavskii, Statistical Irreversibility in Nonlinear Systems [in Russian], Nauka, Moscow (1970).
B.V. Chirikov, Nonlinear Resonance [in Russian], Izd. Novosibirskogo Univ., Novosibirsk (1977).
V.P. Reutov, “Plasma hydrodynamics analogy and the nonlinear stage of vortex wave instability,” Izv. Akad. Nauk SSSR, Fiz. Atm. i Okeana, 16, 1266–1275 (1980).
A.A. Andronov and A.L. Fabrikant, “Landau damping, vortex waves, and surf” in: Nonlinear Waves [in Russian], Nauka, Moscow (1979), p.68.
R. Betchov and W.O. Criminale, Stability of Parallel Flows [Russian translation], Mir, Moscow (1971).
V.D. Shapiro and V.I. Shevchenko, “Wave-particle interactions in nonequilibrial media,” Izv. Vuzov: Radiofiz., 19, 767 (1976).
R.V. Khokhlov, “On the propagation of waves in nonlinear dispersing lines,” Radio i Elekt., 6, 1116 (1961).
R.V. Khokhlov, “Towards the theory of shock waves in nonlinear lines,” Radio i Elekt., 6, 917 (1961).
G.M. Zaslavskii, Stochasticity of Dynamic Systems [in Russian], Nauka, Moscow (1984), chs.1–4.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1989 Kluwer Academic Publishers
About this chapter
Cite this chapter
Rabinovich, M.I., Trubetskov, D.I. (1989). The Nonlinear Oscillator. In: Oscillations and Waves. Mathematics and Its Applications (Soviet Series), vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1033-1_13
Download citation
DOI: https://doi.org/10.1007/978-94-009-1033-1_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6956-4
Online ISBN: 978-94-009-1033-1
eBook Packages: Springer Book Archive