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May/June 2015 On the spectral stability of periodic waves of the Klein-Gordon equation
Aslihan Demirkaya, Sevdzhan Hakkaev, Milena Stanislavova, Atanas Stefanov
Differential Integral Equations 28(5/6): 431-454 (May/June 2015).

Abstract

The object of study is the Klein-Gordon equation in $1+1$ dimensions, with integer power non-linearities. In particular, of interest is the spectral stability/instability (with respect to perturbations of the same period) of traveling-standing periodic solitons, which are of cnoidal ($p=2$), dnoidal ($p=3$) or more general type ($p=5$). The corresponding linearized problem for this two-parameter family of solutions fits the general abstract framework of spectral stability for second order Hamiltonian systems, recently developed by the last two authors and Bronski-Johnson-Kapitula. It is worth noting that the spatial periodicity however, forces a relation between the speed and the phase, which results in some unique challenges in the computations of the quantities involved in the stability index. Our results generalize recent work on the simpler case of standing waves of Natali-Pastor, [9] and Natali-Cardoso, [10].

Citation

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Aslihan Demirkaya. Sevdzhan Hakkaev. Milena Stanislavova. Atanas Stefanov. "On the spectral stability of periodic waves of the Klein-Gordon equation." Differential Integral Equations 28 (5/6) 431 - 454, May/June 2015.

Information

Published: May/June 2015
First available in Project Euclid: 30 March 2015

zbMATH: 1340.35209
MathSciNet: MR3328129

Subjects:
Primary: 35B35 , 35C07 , 35L71

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 5/6 • May/June 2015
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