Analytic solution of the system of two coupled differential equations with the fifth-order non-linearity

L. Cveticanin

Physica A: Statistical Mechanics and its Applications, 2003, vol. 317, issue 1, 83-94

Abstract: In this paper an approximate method for solving a system of two coupled second-order non-linear differential equation with strong and weak non-linearity is developed. The strong non-linearities are of the third and of the fifth order. The suggested new method is partially based on the elliptic-Krylov–Bogolubov method and on the power series method developed for solving the weak non-linear differential equations. The one-frequency solution is considered for the case of certain relations between the equation parameters p and m, and initial conditions. As a special case the oscillatory motion of the physical system described with a fourth-order strong non-linear differential equation is considered. A wide analysis of the corresponding equation is done. The results of the suggested analytic procedure are compared with numerical ones. They show a good agreement.

Keywords: Non-linear vibrations; Fourth-order differential equation (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:317:y:2003:i:1:p:83-94

DOI: 10.1016/S0378-4371(02)01323-7

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