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

Journal Article · Thu Apr 30 00:00:00 EDT 1998 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM1998V189N03ABEH000307; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202769

Kolesov, Yu S ^[1]

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1. P.G. Demidov Yaroslavl State University, Yaroslavl (Russian Federation)

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.

• OSTI ID: 21202769
• Journal Information: Sbornik. Mathematics, Vol. 189, Issue 3; Other Information: DOI: 10.1070/SM1998v189n03ABEH000307; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY-VALUE PROBLEMS
COMPLEX MANIFOLDS
ELASTICITY
EQUATIONS
EQUILIBRIUM
MATHEMATICAL SOLUTIONS
OSCILLATIONS
STABILITY