Viscosity, rogue waves, and permanent downshift in nonlinear Schrodinger models

In this talk we consider the impact of viscosity on the stabilization of spatially periodic breathers (SPBs), related rogue wave activity, and permanent downshift in the framework of a higher order nonlinear Schrodinger (HONLS) model. The Floquet spectral theory of the NLS  equation is used to characterize
the perturbed dynamics in terms of nearby solutions of the NLS equation.
Bands of complex spectrum in the Floquet decomposition of the viscous HONLS data shrink almost to complex points indicating the breakup of the SPB into a
soliton-like structure. Rogue waves in the viscous HONLS flow are found to
typically occur when the spectrum is in a one or more soliton-like  configuration. 
Rogue wave activity in the viscous HONLS is compared with  results  on the emergence of soliton-like rogue waves in a nonlinear damped HONLS model.
Although permanent frequency downshift is observed in both the viscous and nonlinear damped HONLS models, there are important differences in their respective impact on the growth of instabilities.