STABLE SELF-EXCITATIONS OF THE NONLINEAR WAVE EQUATION OF VAN DER POL TYPE.

R. W. Lardner; G. Nicklason

doi:10.1137/0141039

STABLE SELF-EXCITATIONS OF THE NONLINEAR WAVE EQUATION OF VAN DER POL TYPE.

R. W. Lardner^*
, G. Nicklason

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The weakly nonlinear wave equation in which the nonlinearity is of the van der Pol type is considered. This equation has been proposed as a model for the wind-induced oscillations of overhead power lines. It is shown that any initial disturbance generates a solution of finite amplitude which consists of the superposition of two traveling waves having sawtooth profiles. A stability analysis provides a complete classification of all such waves which can be generated.

Original language	English
Pages (from-to)	480-492
Number of pages	13
Journal	SIAM Journal on Applied Mathematics
Volume	41
Issue number	3
DOIs	https://doi.org/10.1137/0141039
State	Published - 1981

ASJC Scopus subject areas

Applied Mathematics

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10.1137/0141039

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@article{50d1dc281bf04608bf2806bec98df5f7,

title = "STABLE SELF-EXCITATIONS OF THE NONLINEAR WAVE EQUATION OF VAN DER POL TYPE.",

abstract = "The weakly nonlinear wave equation in which the nonlinearity is of the van der Pol type is considered. This equation has been proposed as a model for the wind-induced oscillations of overhead power lines. It is shown that any initial disturbance generates a solution of finite amplitude which consists of the superposition of two traveling waves having sawtooth profiles. A stability analysis provides a complete classification of all such waves which can be generated.",

author = "Lardner, \{R. W.\} and G. Nicklason",

year = "1981",

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journal = "SIAM Journal on Applied Mathematics",

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AU - Nicklason, G.

PY - 1981

Y1 - 1981

N2 - The weakly nonlinear wave equation in which the nonlinearity is of the van der Pol type is considered. This equation has been proposed as a model for the wind-induced oscillations of overhead power lines. It is shown that any initial disturbance generates a solution of finite amplitude which consists of the superposition of two traveling waves having sawtooth profiles. A stability analysis provides a complete classification of all such waves which can be generated.

AB - The weakly nonlinear wave equation in which the nonlinearity is of the van der Pol type is considered. This equation has been proposed as a model for the wind-induced oscillations of overhead power lines. It is shown that any initial disturbance generates a solution of finite amplitude which consists of the superposition of two traveling waves having sawtooth profiles. A stability analysis provides a complete classification of all such waves which can be generated.

UR - https://www.scopus.com/pages/publications/0019696990

U2 - 10.1137/0141039

DO - 10.1137/0141039

M3 - Article

AN - SCOPUS:0019696990

SN - 0036-1399

VL - 41

SP - 480

EP - 492

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 3

ER -

STABLE SELF-EXCITATIONS OF THE NONLINEAR WAVE EQUATION OF VAN DER POL TYPE.

Abstract

ASJC Scopus subject areas

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