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Title:
Complex wave regimes in distributed dynamic systems /Review/
Authors:
ZELDOVICH, IA. B.; MALOMED, B. A.
Affiliation:
AB(Akademiia Nauk SSSR, Institut Khimicheskoi Fiziki, Moscow, USSR)
Journal:
Radiofizika, vol. 25, no. 6, 1982, p. 591-618. In Russian.
Publication Date:
00/1982
Category:
Physics (General)
Origin:
STI
NASA/STI Keywords:
DISTRIBUTED PARAMETER SYSTEMS, DYNAMIC RESPONSE, NONSTABILIZED OSCILLATION, SELF OSCILLATION, STABLE OSCILLATIONS, WAVE EQUATIONS, BRANCHING (MATHEMATICS), COMBUSTION STABILITY, COMPLEX SYSTEMS, NONLINEAR EQUATIONS, PERTURBATION THEORY, SCHROEDINGER EQUATION
Bibliographic Code:
1982RaF....25..591Z

Abstract

The work describes some very general types of bifurcations observed in distributed dynamic systems (primarily oscillatory, i.e., with a complex increment but not stochastic) and nonlinear spatial wave regimes arising as a result of these bifurcations. Particular attention is given to an oscillatory instability stabilized by a cubic nonlinearity (a situation that arises in unsteady gasless combustion). In addition, two simple mechanisms of stabilization are examined for the Turing instability. A distributed trigger system with an aperiodically unstable intermediate state is considered, and the role of topological invariants in certain one- and two-dimensional problems is discussed. Finally, a simple nontrivial dynamic system with stochastic behavior is described, and the perturbation theory for the nonlinear Schroedinger equation in the solitonless sector is formulated. 
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