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Oscillators with anharmonic interaction terms

I'm looking for papers modeling oscillators coupled with anharmonic interaction terms. The term is combination of a linear element and a Gaussian kernel that decays proportionally to the difference of ...
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When is this integral zero?

I have a particle with total energy $E$ confined in a potential $$U(x) = -\frac{\cos^4x}{2} - m \cos x - f \sin x. $$ The constants $f$ and $m$ are both in the range (-2,2). The energy is such that ...
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Does sound absorption depends upon the amplitude of sound wave?

I can understand the mechanism of frequency dependant sound absorption by most materials but does the sound attenuation also depends upon the AMPLITUDE(sound pressure or rather loudness/sound ...
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Stationary Perturbation Theory : Estimating higher order corrections for anharmonic oscillator

Note $\hbar = 1$. $$H = H_0 + \lambda V =\frac{p^2}{2m} + m\omega^2x^2 + \lambda m^2\omega^3 x^4$$ Supposedly the perturbation expansion diverges. We are supposed to estimate for what order we have a ...
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Anharmonic oscillators: why is $F=-k x-k' x^3$, with no quadratic terms?

The equation of motion of a general anharmonic oscillator includes a position-dependent force that can be expanded in a Taylor series as $$m\ddot{x}+2\mu\dot{x}+k_0+k_1x+k_2x^2+k_3x^3\ldots=F.$$ I ...