Zhen Zhao and Dmitry E. Pelinovsky
Algebraic dark solitons versus rogue waves in the massive Thirring model
Abstract:
We address the existence of algebraically decaying solitary waves on the
nonzero wave background in the massive Thirring model (MTM) in laboratory coordinates.
We find the precise condition of the spectral stability and instability of the nonzero
wave background. In the case of instability, we distinguish modulational, side-band, and
full-band instabilities and show that the rogue wave exists if and only if the nonzero wave
background is modulationally unstable. For the other unstable cases and in the case of
stability, we show that there exist exactly two algebraic dark solitons which correspond to
the end points in the admissible range of the wave speed for the dark soliton propagation.
Keywords:
massive Thirring model; algebraic dark solitons; rogue waves; stability of the nonzero background.