Chirped envelope optical solitons for Kaup–Newell equation

We investigate the Kaup-Newell equation that represents one of the forms of derivative nonlinear Schrödinger equation. The model applies to the description of sub-pico-second pulse propagation through an optical fiber. A special complex envelope traveling-wave method is applied to find a nonlinear equation with a fifth-degree nonlinear term describing the dynamics of field amplitude in the nonlinear media. It is shown that the phase associated to the obtained pulses has a nontrivial form and possesses two intensity dependent chirping terms in addition to the simplest linear contribution. A class of soliton solutions of the bright, dark and singular type are derived for the first time. The requirements concerning the optical material parameters for the existence of these chirped structures are also discussed.