Chirped Domain Wall Arrays and Solitary Waves in a Generalized Nonlinear Schroedinger Equation

We study a generalized nonlinear Schroedinger equation, and obtain some exact solutions, including domain wall arrays (periodic solutions in terms of elliptic functions), fronts, bright and dark solitons. In certain parameter domains, fundamental bright and dark solitons show directionality and hence are chiral, and the propagation direction is determined by the sign of the self-steepening parameter. Moreover, the chirping reversal phenomena of bright and dark solitons are found. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)