Geodesic
Hamilton's instability index and applications to periodic waves
Mathematics and Education in Mathematics, Tome 50 (2021), pp. 102-110.

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In this survey we present some results on the stability of periodic waves. The main objective is to study their stability with respect to co-periodic perturbations. In our considerations, we rely on an instability index count theories, which in turn critically depend on a detailed spectral analysis of a self-adjoint both scalar and matrix Hill operators, and in the computations of the quantities involved on the stability index.
Keywords: periodic traveling waves, linear stability, nonlinear wave equation, 35B35, 35B40, 35G30 
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     title = {Hamilton's instability index and applications to periodic waves},
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Hakkaev, Sevdzhan. Hamilton's instability index and applications to periodic waves. Mathematics and Education in Mathematics, Tome 50 (2021), pp. 102-110. http://geodesic.mathdoc.fr/item/MEM_2021_50_a9/