Geodesic
A~nonlinear oscillation model with separation of variables
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 349-360

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This paper deals with one-dimensional and two-dimensional oscillatory systems. The theorem about separation of spatial and time variables for this problem is proved. The ODE system for the Fourier coefficients of the solution was found. Numerical experiments with a one-dimensional oscillatory system point to the existence of other oscillations – the energy oscillations inside some cluster of harmonics. 
@article{SJVM_2007_10_4_a2,
     author = {Yu. I. Kuznetsov},
     title = {A~nonlinear oscillation model with separation of variables},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {349--360},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2007_10_4_a2/}
}
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Yu. I. Kuznetsov. A~nonlinear oscillation model with separation of variables. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 349-360. http://geodesic.mathdoc.fr/item/SJVM_2007_10_4_a2/