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Harmonic balance approach for a degenerate torus of a nonlinear jerk equation

✍ Scribed by H.P.W. Gottlieb

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
123 KB
Volume
322
Category
Article
ISSN
0022-460X

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✦ Synopsis

The method of harmonic balance is used for the first time to find approximate expressions for the frequency and displacement amplitude of a degenerate torus arising in a third-order nonlinear oscillator, for a range of velocity amplitudes. The estimates compare favourably with numerically determined solutions. This development complements earlier works on the simpler situations of centres and limit cycles.

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The present paper deals with the mixed boundary value problem for a nonlinear elliptic equation with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the uniqueness and existence of solutions of the above problem for the nonlin