Exact superregular breather solutions to the generalized nonlinear Schrödinger equation with nonhomogeneous coefficients and dissipative effects.

Abstract

Superregular breathers are peculiar solutions to the integrable nonlinear Schrödinger equation that constitute the building blocks for analysis of the nonlinear stage of modulation instability developing from a localized perturbation on the nonvanishing condensate background. Here superregular breather solutions are extended to the generalized nonlinear Schrödinger equation with nonhomogeneous coefficients and in the presence of dissipation. Concrete examples are shown that may allow observation of new solutions in fiber optics where dissipation is unavoidable, nonhomogeneous spatial distribution of the amplification profile can be controlled, and current technology allows design of the longitudinal dispersion profile.