Geodesic
Asymptotic Methods of Investigation of Periodic Solutions of Nonlinear Hyperbolic Equations
Informatics and Automation, Asymptotic methods of investigation of periodic solutions of nonlinear hyperbolic equations, Tome 222 (1998), pp. 3-191.

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The work deals with the asymptotic theory of time periodic solutions of hyperbolic type partial differential equations which simulate oscillation processes in self-excited oscillators with distributed parameters. Peculiarities of the dynamics of the equations in question, including gradient catastrophes, are established and the part played by resonance as a source of relaxation oscillation is revealed. The bufferness phenomenon observed in physical systems is theoretically justified. The work is intended for researchers, higher school teachers, post-graduates who deal with differential equations and their applications, and for specialists who are interested in mathematical, physical and engeneering problems of the oscillation theory. 
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     author = {A. Yu. Kolesov and E. F. Mishchenko and N. Kh. Rozov},
     title = {Asymptotic {Methods} of {Investigation} of {Periodic} {Solutions} of {Nonlinear} {Hyperbolic} {Equations}},
     journal = {Informatics and Automation},
     pages = {3--191},
     publisher = {mathdoc},
     volume = {222},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_1998_222_a0/}
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A. Yu. Kolesov; E. F. Mishchenko; N. Kh. Rozov. Asymptotic Methods of Investigation of Periodic Solutions of Nonlinear Hyperbolic Equations. Informatics and Automation, Asymptotic methods of investigation of periodic solutions of nonlinear hyperbolic equations, Tome 222 (1998), pp. 3-191. http://geodesic.mathdoc.fr/item/TRSPY_1998_222_a0/