Impact of higher-order effects on the dynamics of soliton solutions in the (3+1)D cubic-quintic-septic complex Ginzburg–Landau equation with higher-order dispersion terms

Abstract

We investigate the influence of the higher-order correction term of the nonlinear refractive index and the nonlinear-gain absorption on the dynamics of soliton solutions in a three-dimensional (3D) dissipative medium described by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg–Landau [(3+1)D CQS-CGL] equation with the viscous (spectral-filtering) term, self steepening, Raman effect, dispersion terms up to six, diffraction and cubic-quintic-septic nonlinearities. By mean of direct numerical simulation of the dynamical model, we show that these two parameters can have a significant impact on the dynamics of solitons govern by the above mentioned equation, since their formation deeply depends of the value of each of the above cited parameters. Some interesting particular cases have been detected concerning the combined action of the two parameters or the isolated action of each of them. Among those solutions, we have bell-shaped, snail and creeping dissipative solitons. Also, we have found that the propagation distance z is another important parameter which has allowed us to appreciate the impact of each parameter. At a given distance z or for different values of z, the formation of soliton depends on the value of the higher-order correction term and the nonlinear-gain absorption involved. We have also shown that the above solutions can be self-trapped over a huge propagation distance even in the presence of random perturbations. The discovered nonlinear dependence of the higher-order correction term and the nonlinear-gain absorption on the soliton solution can also be used for the better understanding of the (3+1)D dissipative light bullets in a doped nonlinear kerr medium.