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

Abstract

We have demonstrated numerically 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 higher-order (3 + 1)-dimensional cubic-quintic-septic complex Ginzburg-Landau equation with higher-order effects such as stimulated Raman scattering, self-steepening and third-, fourth-, fifthand sixth-order dispersion terms. These solutions remain localized and can be self-trapped over a huge propagation distance, even in the presence of random perturbations, due to the combined influence of dispersion, diffraction, gain, loss, spectral filtering, the Raman effect and cubic-quintic-septic nonlinearities.

Nonlinear dissipative wave trains in a system of self-propelled particles

“…where with S 0r , S 0i , P 0r , P 0i , T 0r , T 0i , Q 0r , and Q 0i being given in the Appendix. The CGL equation has the merit to describe long-wavelength modulation of both traveling and homogeneous dissipative waves and finds its applications in a wide variety of physical settings such as optical fiber and lasers [46][47][48][49], metamaterials [50,51], Bose-Einstein condensates [52,53], neural and ecological networks [54][55][56][57], blood flow and circulation [58,59], to cite a few. The calculations performed in this work testify that the CGL equations can describe complex biophysical phenomena such as active particle flows and self-assembly of colloidal particles.…”