Geodesic
Existence of countably many stable cycles in media with dispersion
Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 579-595.

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The problem in the title is analyzed in two typical examples of equations with dispersion: the Korteweg–de Vries equation, and the equation for vibrations of a beam. Also, features of the dynamics are considered for the Boussinesq equation, which does not have dispersion. 
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A. Yu. Kolesov. Existence of countably many stable cycles in media with dispersion. Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 579-595. http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a4/

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