Geodesic
Invariant tori for a class of nonlinear evolution equations
Sbornik. Mathematics, Tome 204 (2013) no. 6, pp. 824-868 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper looks at quite a wide class of nonlinear evolution equations in a Banach space, including the typical boundary value problems for the main wave equations in mathematical physics (the telegraph equation, the equation of a vibrating beam, various equations from the elastic stability and so on). For this class of equations a unified approach to the bifurcation of invariant tori of arbitrary finite dimension is put forward. Namely, the problem of the birth of such tori from the zero equilibrium is investigated under the assumption that in the stability problem for this equilibrium the situation arises close to an infinite-dimensional degeneracy. Bibliography: 28 titles.
Keywords: nonlinear wave equation, stability, boundary value problem.
Mots-clés : invariant torus, bifurcation 
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A. Yu. Kolesov; N. Kh. Rozov. Invariant tori for a class of nonlinear evolution equations. Sbornik. Mathematics, Tome 204 (2013) no. 6, pp. 824-868. http://geodesic.mathdoc.fr/item/SM_2013_204_6_a2/

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