The general objective of the work is to study dynamics of dissipative solitons in the
framework of a one-dimensional complex Ginzburg-Landau equation (CGLE) of a fractional …

In this paper, we obtain monotonicity and one-dimensional symmetry of entire solutions to
fractional reaction-diffusion equations by introducing a sliding method, and thus prove the …

This paper proposes and analyzes an efficient difference scheme for the nonlinear complex
Ginzburg–Landau equation involving fractional Laplacian. The scheme is based on the …

In this paper, we first construct an appropriate new generating function, and then based on
this function, we establish a fourth-order numerical differential formula approximating the …

In this paper, we propose a linearized implicit finite difference scheme for solving the
fractional Ginzburg-Landau equation. The scheme, which involves three time levels, is …

In this paper, we are concerned with the numerical solution of the nonlinear fractional
Ginzburg–Landau equation. Galerkin finite element method is used for the spatial …

In this work, we study numerically two-dimensional nonlinear spatial fractional complex
Ginzburg–Landau equations. A centered finite difference method is exploited to discretize …

This paper studies the bifurcations of the exact solutions for the time–space fractional
complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, for …

In this article, an efficient difference scheme for the coupled fractional Ginzburg–Landau
equations with the fractional Laplacian is studied. We construct the discrete scheme based …

This paper proposes and analyzes a high-order implicit-explicit difference scheme for the
nonlinear complex fractional Ginzburg–Landau equation involving the Riesz fractional …