Abnormal single or composite dissipative solitons generation

Abstract The evolution dynamics of the initial finite energy Airy pulses and Airy pulse pairs are numerically investigated in the cubic–quintic complex Ginzberg–Laudau equation governed dissipative system. Depending on different initial excitations and system parameters, abnormal double, triple, and quadruple composite dissipative solitons as well as single dissipative solitons can be observed. The composite dissipative solitons may consist of identical or different types of pulsating solitons. Moreover, the creeping solitons and the single ordinary pulsating solitons can even appear in the parameter regions where originally the other types of pulsating solitons exist. Besides, before evolving into each abnormal dissipative soliton, the initial finite energy Airy pulse or pulse pairs generally exhibit very interesting and unique early evolution behavior.