Dissipative optical bullets modeled by the cubic-quintic-septic complex Ginzburg-Landau equation with higher-order dispersions

We investigate the propagation of dissipative optical bullets under the combined influence of dispersion, diffraction, gain, loss, spectral filtering, Raman effect and cubic-quintic-septic nonlinearities. Using the Maxwell equations, we derive a basic equation modeling the propagation of ultrashort optical solitons in optical fiber, named the higher-order (3+1)D cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation. Considering this higher-order (3+1)D CQS-CGL equation, we use a variational approach to obtain a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations that we obtained are investigated numerically in order to observe the behavior of pulse parameters along the optical fiber. A fully direct numerical simulation of the higher-order (3+1)D CQS-CGL equation finally tests the results of the variational approach. A good agreement between analytical and numerical methods is observed. Among different behaviors, bell-shaped dissipative light bullets, double, triple and quadruple bullet complexes are obtained under certain parameter values for anomalous, zero and normal chromatic dispersion regimes.