Numerical simulation of blow-up of a 2D generalized Ginzburg-Landau equation Original Research Article

We study the Cauchy problem for the following generalized Ginzburg-Landau equation ut = (ν+iα)Δu − (κ+iβ)|u|2qu + γu in two spatial dimensions for q > 1 (here α, β, γ are real parameters and ν,κ > 0). A blow-up of solutions is found via numerical simulation in several cases for q > 1.