Flat blow-up solutions for the complex Ginzburg Landau equation

Giao Ky Duong, Nejla Nouaili, Hatem Zaag

In this paper, we consider the complex Ginzburg-Landau equation $${\partial }_{t}u=(1+i{\hat{I}}^2)\hat{I}”u+(1+i\hat{I}´)|u{|}^{p-1}u-\hat{I}\pm u,\text{where }{\hat{I}}^2,\hat{I}´,\hat{I}\pm \in \mathbb{R}.$$ The…