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Title: Parametric oscillations of a singularly perturbed telegraph equation with a pendulum non-linearity

The solution of the problem in the title is reduced to an analysis of the question of the number of and stability of equilibrium states of the quasi-normal form of the boundary-value problem under consideration. A mechanism is revealed for the origin of its so-called simple equilibrium states. It is shown that as the coefficient of elasticity decreases, the number of such states increases, and that those of them with the most complex spatial structure are stable.
Authors:
 [1]
  1. P.G. Demidov Yaroslavl State University, Yaroslavl (Russian Federation)
Publication Date:
OSTI Identifier:
21202769
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 189; Journal Issue: 3; Other Information: DOI: 10.1070/SM1998v189n03ABEH000307; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY-VALUE PROBLEMS; COMPLEX MANIFOLDS; ELASTICITY; EQUATIONS; EQUILIBRIUM; MATHEMATICAL SOLUTIONS; OSCILLATIONS; STABILITY