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

abstract

• 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.

authors

• Berkolaiko, Gregory
• Comech, Andrew

published proceedings

• NONLINEARITY

author list (cited authors)

• Berkolaiko, G., Comech, A., & Sukhtayev, A.

citation count

• 11

complete list of authors

• Berkolaiko, Gregory||Comech, Andrew||Sukhtayev, Alim

publication date

• January 2015

publisher

• IOP Publishing  Publisher

published in

• NONLINEARITY  Journal

keywords

• Gross-neveu Model
• Linear Stability
• Massive Thirring Model
• Nonlinear Dirac Equation
• Solitary Waves
• Vakhitov-kolokolov Criterion

Digital Object Identifier (DOI)

• 10.1088/0951-7715/28/3/577

start page

• 577

end page

• 592

volume

• 28

issue

• 3

URL

• http://dx.doi.org/10.1088/0951-7715/28/3/577