In Fall 2026, the seminar meets in Blocker 302 on Thursdays at 4pm.

2026Fall

  • September 24, 2026

    Andrew Comech, TAMU

    Title: Complete characterization of linear stability for nonlinear Dirac equation in 1D

    Abstract: One says that a solitary wave solution is “spectrally stable” if the operator of linearization at this wave has no eigenvalues with positive real part. In the case of the nonlinear Dirac equation, this question becomes very convoluted in view of possibility of “quadruplets” of complex eigenvalues, with nonzero real and imaginary parts. We finally show that in 1D this never happens; the spectral stability is completely characterized by the Vakhitov–Kolokolov condition (dQ/d\omega<0) and the energy vanishing condition (E>0). This is the introductory talk; no prior acquaintance with Dirac is assumed.