Approximate first integrals of weakly nonlinear, damped-driven oscillators with one degree of freedom

被引：7

作者：

Ünal, G ^{[1
]}

机构：

[1] Istanbul Tech Univ, Fac Sci & Letters, TR-80626 Istanbul, Turkey

来源：

NONLINEAR DYNAMICS | 2001年 / 26卷 / 04期

关键词：

approximate symmetries; resonances; approximate first integrals; bifurcations;

D O I：

10.1023/A:1013331523696

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

First-order approximate symmetries of weakly nonlinear, damped-driven oscillators have been determined. First-order approximate first integrals have been obtained by employing an approximate version of Noether's theorem for the conservative case. Furthermore, approximate first integrals of the damped case have been obtained based on the first integrals of the conservative case. Approximate first integrals enabled us to identify three types of generic bifurcations. Analytical results have been verified by numerical experiments.

引用

页码：309 / 329

页数：21

共 7 条

[1] Approximate First Integrals of Weakly Nonlinear, Damped-Driven Oscillators with One Degree of Freedom
Gazanfer Unal
Nonlinear Dynamics, 2001, 26 : 309 - 329
[2] Traveling solitons in the damped-driven nonlinear Schrodinger equation
Barashenkov, IV
Zemlyanaya, EV
SIAM JOURNAL ON APPLIED MATHEMATICS, 2004, 64 (03) : 800 - 818
[3] Approximate partial Noether operators and first integrals for coupled nonlinear oscillators
I. Naeem
F. M. Mahomed
Nonlinear Dynamics, 2009, 57 : 303 - 311
[4] Approximate partial Noether operators and first integrals for coupled nonlinear oscillators
Naeem, I.
Mahomed, F. M.
NONLINEAR DYNAMICS, 2009, 57 (1-2) : 303 - 311
[5] Approximate partial Noether operators and first integrals for cubically coupled nonlinear Duffing oscillators subject to a periodically driven force
Naz, R.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 380 (01) : 289 - 298
[6] On approximations of first integrals for strongly nonlinear oscillators
Waluya, SB
Van Horssen, WT
NONLINEAR DYNAMICS, 2003, 32 (02) : 109 - 141
[7] On Approximations of First Integrals for Strongly Nonlinear Oscillators
S. B. Waluya
W. T. van Horssen
Nonlinear Dynamics, 2003, 32 : 109 - 141

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