Dynamics of moving cavity solitons in two-level laser system from symmetric gaussian input: vectorial cubic-quintic complex Ginzburg–Landau equation

Dynamics of vortex and anti-vortex solitons in a vectorial cubic-quintic complex Ginzburg-Landau equation

“…To explore the dynamics of VVSs defined here by the envelope of the electromagnetic field such as ψ ± (r, θ, t), we consider the following coupled (2+1)D CCQGLVEs [46,48,65] y y y y y g y y n y y d y y y y…”

“…The derivation of our current model begins with the MBEs, describing the propagation of a slowly varying field envelope through a collection of two-level atoms. Importantly, we do not assume a fixed direction for the transverse electric field within the laser cavity [48]. The nonlinear polarization obtained from our derivation is of third order, comprising three terms Among these terms, we specifically focus on the quintic nonlinearities present in the current model [48].…”

“…Importantly, we do not assume a fixed direction for the transverse electric field within the laser cavity [48]. The nonlinear polarization obtained from our derivation is of third order, comprising three terms Among these terms, we specifically focus on the quintic nonlinearities present in the current model [48]. This form of nonlinear polarization corresponds to materials exhibiting a higher degree of spatial symmetry (such as isotropic materials; see [69]).…”

“…To study theoretically and numerically the dynamics of optical solitons in waveguides both in the spatial and the temporal domains, various analytical approaches such as the collective variable technique [42,43], the variational approaches (VAs) [44][45][46][47][48], perturbation technique through the analysis of the modulational instability (MI) phenomenon [49][50][51], the direct simulation of continuous, semi-discrete or discrete solutions [52][53][54] can be used.…”

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.…”