| Abstract: |
| The stability and dynamical properties of the so-called resonant nonlinear
Schr\odinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear
Schr\odinger (NLS) equation with the addition of a perturbation used to describe wave
propagation in cold collisionless plasmas. We first examine the modulational stability
of plane waves in the RNLS model, identifying the modifications of the associated
conditions from the NLS case. We then move to the study of solitary waves with
vanishing and nonzero boundary conditions. Interestingly the RNLS, much like the usual
NLS, exhibits both dark and bright soliton solutions depending on the relative signs of
dispersion and nonlinearity. The corresponding existence, stability and dynamics of
these solutions are studied systematically. |
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