Dark soliton solutions of the cubic-quintic complex Ginzburg–Landau equation with high-order terms and potential barriers in normal-dispersion fiber lasers

In this paper, we numerically study dark solitons in normal-dispersion optical fibers described by the cubic-quintic complex Ginzburg–Landau equation. The effects of the third-order dispersion, self-steepening, stimulated Raman dispersion, and external potentials are also considered. The existence, chaotic content and interactions of these objects are analyzed, as well as the tunneling through a potential barrier and the formation of dark breathers aside from dark solitons in two dimensions and their mutual interactions as well as with periodic potentials. Furthermore, the homogeneous solutions of the model and the conditions for their stability are also analytically obtained.

Highly Dispersive Optical Solitons with Complex Ginzburg–Landau Equation Having Six Nonlinear Forms

This paper retrieves highly dispersive optical solitons to complex Ginzburg–Landau equation having six forms of nonlinear refractive index structures for the very first time. The enhanced version of the Kudryashov approach is the adopted integration tool. Thus, bright and singular soliton solutions emerge from the scheme that are exhibited with their respective parameter constraints.

New Explicit and Exact Traveling Waves Solutions To The Modified Complex Ginzburg Landau Equation

This paper applies function transformation method to obtain under certain conditions bright, dark, kink and W-shaped dark solitons waves solutions to the modified complex Ginzburg Landau Equation (CGLE). These new obtained solutions can be useful in many applications such as communication, medicine, hydrodynamic, thermodynamic just to name a few and can allow to explain physical phenomena.

Spectral stability of pattern-forming fronts in the complex Ginzburg–Landau equation with a quenching mechanism

We consider pattern-forming fronts in the complex Ginzburg–Landau equation with a traveling spatial heterogeneity which destabilises, or quenches, the trivial ground state while progressing through the domain. We consider the regime where the heterogeneity propagates with speed c just below the linear invasion speed of the pattern-forming front in the associated homogeneous system. In this situation, the front locks to the interface of the heterogeneity leaving a long intermediate state lying near the unstable ground state, possibly allowing for growth of perturbations. This manifests itself in the spectrum of the linearisation about the front through the accumulation of eigenvalues onto the absolute spectrum associated with the unstable ground state. As the quench speed c increases towards the linear invasion speed, the absolute spectrum stabilises with the same rate at which eigenvalues accumulate onto it allowing us to rigorously establish spectral stability of the front in L 2 ( R ) . The presence of unstable absolute spectrum poses a technical challenge as spatial eigenvalues along the intermediate state no longer admit a hyperbolic splitting and standard tools such as exponential dichotomies are unavailable. Instead, we projectivise the linear flow, and use Riemann surface unfolding in combination with a superposition principle to study the evolution of subspaces as solutions to the associated matrix Riccati differential equation on the Grassmannian manifold. Eigenvalues can then be identified as the roots of the meromorphic Riccati–Evans function, and can be located using winding number and parity arguments.

Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries

This paper investigates the effect of gravity modulation on Rayleigh–Bénard convection using the rigid isothermal boundary conditions. We calculate heat transfer results using the Nusselt and mean Nusselt numbers through the finite-amplitude of convection, which we got from the Ginzburg–Landau equation (GLE). The Ginzburg–Landau equation is derived analytically from the Fredholm solvability condition at third order. The finite amplitude equation (GLE) is a function of system parameters and solved numerically. The gravity modulation considered in terms of steady and sinusoidal parts. The sinusoidal part defines gravity modulation in terms of amplitude and frequency. Our study shows that gravity modulation controls the heat transfer results. The amplitude of modulation enhances heat transfer for low frequencies and diminishes for high frequencies. Further, we found that rigid isothermal boundary conditions are diminishing heat transfer than free and isothermal boundaries. Finally, we concluded that rigid isothermal boundary conditions and gravity modulation controls heat transfer results.