Dark and dark-like-bright solitons for a higher-order nonlinear Schrödinger equation in optical fibers

Abstract

In this letter, dark and dark-like-bright solitons will be investigated for a higher-order nonlinear Schrödinger equation with such higher-order effects as the third-order dispersion (TOD), self-steepening (SS) and self-frequency shift, for the ultrashort pulses in the subpicosecond or femtosecond regime. Via the Hirota method and symbolic computation, the bilinear forms are obtained, while the dark single-hump, dark double-hump and dark-like-bright soliton solutions are constructed. Parametric regions for the existence of the three types of solitons are related to the TOD and SS coefficients. When the TOD and SS coefficients change, the amplitudes of the dark single-hump, dark-like-bright solitons and the interval between the two peaks of a dark double-hump soliton will change, while the amplitude of the dark double-hump soliton will be invariant. Through the asymptotic analysis, we prove that the two-soliton interactions are elastic. With the group-velocity-dispersion coefficient changing, the type of the solitons and interactions may change, e.g., from the overtaking interaction to the head-on one. With the TOD and SS coefficients changing, interactions can be seen between i) two dark single-hump solitons, ii) two dark double-hump solitons, iii) one dark single-hump and one dark double-hump solitons, and iv) two dark-like-bright solitons.