Effect of nonlinear gradient terms on breathing localized solutions in the quintic complex Ginzburg-Landau equation

We study the effect of nonlinear gradient terms on breathing localized solutions in the complex Ginzburg-Landau equation. It is found that even small nonlinear gradient terms-which appear at the same order as the quintic term-can cause dramatic changes in the behavior of the solution, such as causing opposite sides of an otherwise monoperiodic symmetrically breathing solution to breathe at different frequencies, thus causing the solution to breathe periodically or chaotically on only one side or the solution to rapidly spread. [S0031-9007(98)07488-2].