The Mathematical Physics Seminar meets in SDRICH 333 on Wednesdays at 2:30 PM.
Upcoming non-local speakers
April 25: Andrew Comech, Texas A&M University and IITP, Russia
Stability of solitary waves in the nonlinear Dirac equation
ABSTRACT:
We consider stability of solitary waves in the nonlinear Dirac equation with the scalar self-interaction, known as the Soler model. We prove that small amplitude solitary waves in the charge-critical and charge-subcritical cases are spectrally stable: the linearization at a solitary wave has no eigenvalues with positive real part. An important part of the stability analysis is the proof of the absence of bifurcations of nonzero-real-part eigenvalues from the embedded threshold points. Our approach is based on constructing a new family of exact bi-frequency solitary wave solutions, on using this family to determine the multiplicity of embedded eigenvalues of the linearized operator, and on the analysis of the behaviour of “nonlinear eigenvalues”: characteristic roots of holomorphic operator-valued functions. The talk is based on the joint work with Nabile Boussaid, University of Besançon — Franche-Comté.
We consider stability of solitary waves in the nonlinear Dirac equation with the scalar self-interaction, known as the Soler model. We prove that small amplitude solitary waves in the charge-critical and charge-subcritical cases are spectrally stable: the linearization at a solitary wave has no eigenvalues with positive real part. An important part of the stability analysis is the proof of the absence of bifurcations of nonzero-real-part eigenvalues from the embedded threshold points. Our approach is based on constructing a new family of exact bi-frequency solitary wave solutions, on using this family to determine the multiplicity of embedded eigenvalues of the linearized operator, and on the analysis of the behaviour of “nonlinear eigenvalues”: characteristic roots of holomorphic operator-valued functions. The talk is based on the joint work with Nabile Boussaid, University of Besançon — Franche-Comté.