Memory function approach to a nonlinear oscillator

Takeo Nishigori

Physica A: Statistical Mechanics and its Applications, 1982, vol. 111, issue 1, 323-333

Abstract: An exact linear equation of motion of the form ẍ(t) + ω2x(t) + ∫t0Λ(t − t′)x(t′)dt′ = 0 proposed for an undamped anharmonic oscillator. A renormalized frequency ω and a memory function Λ(t) reflect the nonlinearity. The laplace transform Λ(z) of the memory function is given by a combination of infinite continued fractions in z2. With a cubic anharmonic oscillator as an example, we show that higher-order memory functions Λn(t), which are associated with Λ(t), oscillate rapidly so that Λn(t) ≡ 0 is a good approximation (cf. the instantaneous decay approximation Λn(t) ∝ δ (t) in dissipative systems).

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:111:y:1982:i:1:p:323-333

DOI: 10.1016/0378-4371(82)90097-8

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