Physical Sciences and Mathematics Commons^™

Solitary Waves Of A Pt-Symmetric Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena, Fred Cooper, Avinash Khare, Andrew Comech, Carl M. Bender

Mathematics and Statistics Department Faculty Publication Series

Abstract—In the present work, we consider a prototypical example of a PT -symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the PT -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the PT -symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the PT - transition threshold. In the latter, they degenerate into linear waves. We also examine the dynamics of …