,Collisions between Solitons Modulated by Gain/Loss and Phase in the Complex Ginzburg-Landau Equatio

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Complex Ginzburg Landau (CGL) equations are well known as basic models of the patte formation in various nonlinear dissipative media.[1-3] An important class of pattes observed in these media and reproduced by the CGL equations is dissipative soliton (DS).[4-6] It is well known that the CGL equation with the cubic-quintic (CQ) nonlinearity can support stable DSs in any dimension.The CGL equation with the cubic-quintic (CQ) nonlinearity was first proposed in a two-dimensional form by Petviashvili and Sergeev[7] as a model generating stable localized modes.In the 1D version of the model,the stable solutions of solitons were investigated in detail.[sl Nonlinear optical media that feature the CQ response include chalcogenide glasses[9]and some organic materials.[10] Subsequently,numerous complex stable pattes in this model have been investigated including stable vortices,[11] stable soliton clusters,[12,13] bound states,[14,15] and novel dynamics by adding an exteal potential.
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