Dynamics of localized symmetric periodical waves in the non-Kerr media

A perturbed higher-order nonlinear Schrödinger equation with self-steepening, self-frequency shift, and quintic non-Kerr nonlinearity terms is used to investigate the dynamics of ultrashort periodical pulses with special symmetries in the non-Kerr media. Via the linear stability analysis, the modulational stability of the continuous-wave background which supports the periodical waves is investigated in details and the analytical expression for the gain spectrum of modulational instability is presented. The effects of various equation parameters (such as the third order dispersion restraint, the quintic non-Kerr nonlinearity parameters, and the self-steepening and self-frequency shift parameters) on the modulational instability are analyzed. We demonstrate that the competing quintic non-Kerr nonlinearity induces propagating periodical waves that show special symmetries such as the mirror- and rotational-symmetry. Parameter domains are delineated in which these optical periodical pulses exist. We show that Khare–Sukhatme superposition procedure can be applied for generating superposition periodical pulses. We further show that the amplitude and the width of the periodical pulses in both anomalous and normal dispersion regimes can be controlled by varying the third order dispersion restraint, the self-steepening term, the self-frequency shift, as well as the quintic non-Kerr nonlinearity terms.