Dissipative soliton dynamics in non-Kerr and Kerr type nonlinear media

We theoretically model a dissipative system which exhibits self-defocussing non-Kerr type of nonlinearity and numerically study the dynamics of dissipative solitons (DSs) whose evolution is governed by a complex Ginzburg-Landau equation (GLE). We show that, the formation of DSs are not restricted by positive nonlinearity and negative dispersion. The DSs can still be excited in normal group velocity dispersion regime, provided the nonlinearity is negative. To study the complete dynamics, we excite DSs in four different nonlinear-dispersive domain i.e., both in the Kerr and non-Kerr type medium (separated by zero nonlinearity wavelength (ZNW)) where the group-velocity dispersion may be normal or anomalous (separated by zero dispersion wavelength). For each case we modify the GLE and rewrite the dissipative system parameters of DS ansatz. We adopt semianalytic variational technique to study the overall pulse dynamics under various perturbations. The spectral and temporal evolutions of the DS induced by the perturbations due to the third-order dispersion (TOD) and higher-order nonlinearities are studied numerically in all four domain and are then compared with variational results. Our semi-analytic results match reasonably well with the numerical results and are useful for gaining physical insight into complex soliton-evolution processes. It is also observed that the frequency of dispersive wave generated due to TOD is also tailored by introducing the ZNW.