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arXiv · 1306.5150

Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields

Gregory Berkolaiko·Andrew Comech·Alim Sukhtayev
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Abstract

We study the linear stability of localized modes in self-interacting spinor fields, analyzing the spectrum of the operator corresponding to linearization at solitary waves. Following the generalization of the Vakhitov--Kolokolov approach, we show that the bifurcation of real eigenvalues from the origin is completely characterized by the Vakhitov--Kolokolov condition $dQ/dω=0$ and by the vanishing of the energy functional. We give the numerical data on the linear stability in the generalized Gross--Neveu model and the generalized massive Thirring model in the charge-subcritical, critical, and supercritical cases, showing the agreement with the Vakhitov--Kolokolov and the energy vanishing conditions.

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Gregory Berkolaiko, Andrew Comech, Alim Sukhtayev. 2014-10-31. Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields. https://arxiv.org/abs/1306.5150

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