Geodesic
The Parametric Buffer Phenomenon for a Singularly Perturbed Telegraph Equation with a Pendulum Nonlinearity
Matematičeskie zametki, Tome 69 (2001) no. 6, pp. 866-875 
A. Yu. Kolesov; N. Kh. Rozov. The Parametric Buffer Phenomenon for a Singularly Perturbed Telegraph Equation with a Pendulum Nonlinearity. Matematičeskie zametki, Tome 69 (2001) no. 6, pp. 866-875. http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a5/
@article{MZM_2001_69_6_a5,
     author = {A. Yu. Kolesov and N. Kh. Rozov},
     title = {The {Parametric} {Buffer} {Phenomenon} for a {Singularly} {Perturbed} {Telegraph} {Equation} with a {Pendulum} {Nonlinearity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {866--875},
     year = {2001},
     volume = {69},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the boundary-value problem $$ u_{tt}+\varepsilon u_t+(1+\varepsilon\alpha\cos 2\tau)\sin u =\varepsilon\sigma^2u_{xx}, \qquad u_x|_{x=0}=u_x|_{x=\pi}=0, $$, where $0<\varepsilon\ll1$, $\tau=(1+\varepsilon\delta)t$, $\alpha,\sigma>0$, and the sign of $\delta$ is arbitrary. It is proved that for an appropriate choice of the external parameters $\alpha$ and $\delta$ and for sufficiently small $\sigma$ the number of exponentially stable solutions $2\pi$-periodic in $\tau$ can be made equal to an arbitrary predefined number.

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