Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields
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2015 IOP Publishing Ltd & London Mathematical Society. We study the linear stability of localized modes in self-interacting spinor fields, analysing 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 d Q/d = 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, charge-critical and chargesupercritical cases, illustrating the agreement with the Vakhitov-Kolokolov and the energy vanishing conditions.