Geodesic
Parametric excitation of high-mode oscillations for a~non-linear telegraph equation
Sbornik. Mathematics, Tome 191 (2000) no. 8, pp. 1147-1169

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The problem of parametric excitation of high-mode oscillations is solved for a non-linear telegraph equation with a parametric external excitation and small diffusion. The equation is considered on a finite (spatial) interval with Neumann boundary conditions. It is shown that under a proper choice of parameters of the external excitation this boundary-value problem can have arbitrarily many exponentially stable solutions that are periodic in time and rapidly oscillate with respect to the spatial variable. 
@article{SM_2000_191_8_a1,
     author = {A. Yu. Kolesov and N. Kh. Rozov},
     title = {Parametric excitation of high-mode oscillations for a~non-linear telegraph equation},
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     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_8_a1/}
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A. Yu. Kolesov; N. Kh. Rozov. Parametric excitation of high-mode oscillations for a~non-linear telegraph equation. Sbornik. Mathematics, Tome 191 (2000) no. 8, pp. 1147-1169. http://geodesic.mathdoc.fr/item/SM_2000_191_8_a1/