Hierarchical Systems with Partial Derivatives. Method of Averaged Characteristics

A.A. Ruhadze, L.S. Bogdankevich, S.E. Rosinkii, V.G. Ruhlin. Physics of high-current relativistic beams. Atomizdat, Moscow, 1980.Google Scholar

R.C. Davidson. Theory of nonlinear plasmas. Mass: Benjamin, Reading, 1974.Google Scholar

A.G. Sitenko and V.M. Malnev. Principles of the plasma theory. Naukova Dumka, Kiev, 1994.Google Scholar

L.A. Vainstein, V.A. Solnzev. Lectures on Microwave electronics. Sov. Radio, Moscow, 1973.Google Scholar

V.I. Gaiduk, K.I. Palatov, D.M. Petrov. Principles of microwave physical electronics. Sov. Radio, Moscow, 1971.Google Scholar

A.F. Alexandrov, L.S. Bogdankevich, A.A. Ruhadze. Principles of plasma electrodynamics. Vyschja Shkola, Moscow, 1978.Google Scholar

A.N. Kondratenko, V.M. Kuklin. Principles of plasma electronics. Energoatomizdat, Moscow, 1988.Google Scholar

B.E. Zshelezovskii. Electron beam parametric microwave amplifiers. Nauka, Moscow, 1971.Google Scholar

I.V. Savel’jev. Principles of theoretical physics. Nauka, Moscow, 1977.Google Scholar

E.M. Liftshitz, L.P. Pitayevskiy. Physical kinetics. Nauka, Moscow, 1979.Google Scholar

I.V. Dzedolik, V.V. Kulish. To the nonlinear theory of parametrical resonance of electromagnetic waves in plasmas of a high-current relativistic electron flux. Ukrainian Physical Journal, 32(11):1672–1677, 1987.Google Scholar

J. Weiland, H. Wilhelmsson. Coherent nonlinear interactions of waves in plasmas. Pergamon Press, Oxford, 1977.Google Scholar

V.V. Kulish, V.I. Savchenko. Method of averaged characteristics in nonlinear electrodynamic problems. Gerald of Sumy State University, ser. Physics and Mathematics, 2:5–12, 2002.Google Scholar

V.V. Kulish, A.V. Lysenko. Method of averaged kinetic equation averaged kinetic equation and its use in the nonlinear problems of plasma electrodynamics. Fizika Plasmy (sov. Plasma Physics), 19(2):216–227, 1993.Google Scholar

V.V. Kulish, P.B. Kosel, A.G. Kailyuk. New acceleration principle of charged particles for electronics applications. the general hierarchical approach. International Journal of Infrared and Millimeter Waves, 19(1):3–93, 1993.Google Scholar

V.V. Kulish. Methods of averaging in nonlinear problems of relativistic electrodynamics. World Federation Publishers, Atlanta, 1998.Google Scholar

V.V. Kulish, V.I. Savchenko. Method of averaged characteristics in the nonlinear theory of two-stream instability two-stream instability. Gerald of Sumy State University, ser. Physics and Mathematics, 2:13–18, 2002.Google Scholar

A.I. Olemskoi, A.Ya. Flat. Application of the factual concept in the condensedmatter physics. Physics-Uspekhy, 163(12):101–104, 1993.Google Scholar

R. Rammal, G. Toulouse, M.A. Virasoro. The gnats and gnus document preparation system. Reviews of Modern Physics, 50(3):765–788, 1986.MathSciNetADSCrossRefGoogle Scholar

F.G. Tricomi. Lezioni sulle equzioni a derivative partziali. Editrice Gheroni Torino via Carlo Alberto, 1954.Google Scholar

G.A. Korn, T.W. Korn. Mathematical handbook for scientists and engineers. NY: McGraw Hill, 1961.MATHGoogle Scholar

A.M. Samoylenko, S.A. Kryvoshyja, N.A. Perestyuk. Differential equations: examples and exercises. Vysshaja Shkola, Moscow, 1989.Google Scholar

A.N. Tichonov, A.B. Vasil’jeva, A.G. Sveshnikov. Differential equations. Nauka, Moscow, 1980.Google Scholar

N.M. Matvejev. Integration methods integration of differential equations. Vysshaja Shkola, Moscow, 1963.Google Scholar

S.K. Godunov. Equations of mathematical physics. Nauka, Moscow, 1971.Google Scholar

V.V. Kulish. Nonlinear self-consistent theory of free electron lasers. method of investigation. Ukrainian Physical Journal, 36(9):1318–1325, 1991.Google Scholar

V.V. Kulish, S.A. Kuleshov, A.V. Lysenko. Nonlinear self-consistent theory of superheterodyne and free electron lasers. The International journal of infrared and millimeter waves, 14(3):451–568, 1993.ADSCrossRefGoogle Scholar

T.C. Marshall. Free electron laser. Mac Millan, New York, London, 1985.Google Scholar

C. Brau. Free electron laser. Academic Press, Boston, 1990.Google Scholar

P. Luchini, U. Motz. Undulators and free electron lasers. Clarendon Press, Oxford, 1990.Google Scholar