Dissipative light bullets: From stationary light bullets to double, quadruple, sixfold, eightfold and tenfold bullet complexes

Robust propagation of optical vortex beams, necklace-ring solitons, soliton clusters and uniform-ring beams generated in the frame of the higher-order (3 + 1)-dimensional cubic–quintic–septic complex Ginzburg–Landau equation

“…It has also been revealed numerically that spatiotemporal necklace-ring solitons carrying zero, integer and even fractional angular momentum can be self-trapped over a huge propagation distance in the three-dimensional cubic-quintic complex Ginzburg-Landau equation [51]. To the best of our knowledge, spatiotemporal-localized structures in highly nonlinear doped Kerr media where higher-order nonlinearity, diffraction and dispersion act on similar footing are less reported, although we discussed the propagation and stabilization of dissipative optical light bullets under the combined influence of dispersion, diffraction, gain, loss, spectral filtering, Raman effect and cubic-quintic-septic nonlinearities in doped Kerr media with higher-order dispersion terms, based on the higher-order (3 + 1)D cubic-quintic-septic complex Ginzburg-Landau [(3 + 1)D CQS-CGL] equation, very recently [52][53][54]. We show that new families of spatiotemporal dissipative optical bullets, including self-trapped necklace-ring, ring-vortex solitons, uniform-ring beams, spherical and rhombic distributions of light bullets, and fundamental and cluster solitons, are possible in the following (3 + 1)D CQS-CGL equation with higher-order effects such as stimulated Raman scattering, self-steepening and third-, fourth-, fifthand sixth-order dispersion terms:…”

Simple harmonic and damped motions of dissipative solitons in two-dimensional complex Ginzburg-Landau equation supported by an external V-shaped potential

“…Kochetov et al studied the evolution of dissipative structures to regime with spontaneous transformation of the topological excitations and logic gates on stationary dissipative solitons in the form of the CGL equation with a potential term [28][29]. Based on the analysis of the high-order (3+1)-dimensional CQ CGL equation, the fourth, sixth, eighth and tenth dissipative bullet complexes were observed using the variational method and the Lyapunov method, and the scalar potential was analyzed to study the stability of optical photon bombs through the medium [30]. Based on the (3+1)-dimensional CQ CGL equation with lateral 2D trap potential, a passive mode-locked laser model based on gradient index nonlinear multimode fiber was studied [31].…”