Breathing solitons for the one-dimensional nonlinear cubic-quintic complex Ginzburg-Landau equation (cqCGLE)

Using one-dimensional nonlinear cubic-quintic complex Ginzburg-Landau equation (cqCGLE), we construct breathing pattern of soliton behaviour with hyperbolic sine and hyperbolic tangent as initial amplitude profile. Breathing pattern of solitons will be discussed in detail during their adjustment phase and self-organization phase. Breathing pattern is observed by means of numerical simulation.