Abstract
We study the propagation properties of nonlinear periodic waves in an optical fiber medium exhibiting Kerr dispersion and quintic nonlinearity. The quintic derivative nonlinear Schr & ouml;dinger equation is applied to model the evolution of femtosecond light waves in such system. Unlike periodic structures in Kerr media, the novel waves possess a nonlinear chirp which varies with their intensity. In addition to the linear part, the pulse chirp also includes two intensity dependent chirping terms. The conditions on fiber parameters for the existence of the newly found periodic waves are presented. A wide variety of solitary pulse shapes including the bright, dark, kink, anti-kink, and gray solitary waves are obtained in the long wave limit. Our results show that Kerr dispersion plays a crucial role in introducing a nonlinear chirp for the periodic and solitary waves. Finally, the stability of these nonlinearly chirped solutions is numerically studied under the finite perturbations.
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