Existence and stability of singular patterns in a fractional Ginzburg–Landau equation with a mean field

Abstract In this paper, we consider the existence and stability of singular patterns in a fractional Ginzburg–Landau equation with mean field. We prove three types steady-state (double fronts, single spikes, double spikes) by solving their respective consistency conditions. case small spike solution for sufficiently large spatial period studying an explicit non-local eigenvalue problem which is equivalent to original problem. For other solutions, instability using variational characterisation eigenvalues. Finally, present results some numerical computations solutions based on finite difference methods Crank–Nicolson Adams–Bashforth.