Cascade Replication Of Soliton Solutions Of One-dimensional Complex Ginzburg-Landau Equation

The "soliton" phenomenon describes that the water wave keeps its shape,amplitude and speed while moving,and lasts for a long time before disappearing.This phenomenon was first discovered by Scottish scientist John Scott Russell.In physics,solitons can be considered as the equilibrium between the nonlinear effect and the dispersion effect in the medium.In mathematics,solitons can be considered as stable solutions of a class of nonlinear partial differential equations describing physical systems.With the development of science and people's in-depth understanding of various microscopic phenomena,more and more soliton phenomena have been discovered,and various nonlinear models have been proposed to describe these phenomena,making the soliton theory widely applied to various fields include biology,nuclear physics,nonlinear optics,condensed matter physics,superconductor physics,etcIn this paper,we briefly review the historical background and research progress of solitons,introduce three types of solitons in Hamiltonian system,and then introduce solitons in dissipative system.The soliton solution of Hamiltonian system is the result of the equilibrium between diffraction(dispersion)and the nonlinearity of the medium.We introduce the complex cubic-quintic Ginzburg-Landau equation in the dissipative system,study the disturbance of the dissipative soliton by external forces,and obtain two meaningful results.1.Waveform transformation based on the complex cubic-quintic Ginzburg-Landau equation Soliton solutions.We first study the waveform transformation based on the complex cubic-quintic Ginzburg-Landau equation Soliton solutions.By increasing the external force on the dissipative soliton,the waveform transformation between different dissipative solitons was changed.The experiment proves that the plain pulse soliton can be converted into periodic pulse soliton under a small external force disturbance,and then the potential potential is disconnected during the evolution of the periodic pulse soliton.Three different situations will occur,namely:conversion into a plain pulse soliton,a composite soliton,or a composite soliton and two plain pulse solitons.Under a large external force disturbance,the plain pulse soliton will be converted into a quasi-period soliton or chaotic soliton.2.Cascade replication based on the complex cubic-quintic Ginzburg-Landau equation Soliton solutions.We study the cascade replication of dissipative solitons based on the complex cubic-quintic Ginzburg-Landau equation.This effect simulates the effect of external forces on dissipative solitons by adding an additional linear term to the equation.Through this effect,a dissipative soliton can replicate to obtain multiple identical dissipative solitons.After that,we improve the theoretical model on the basis of this method,and propose two improved new methods,greatly reducing the time required to copy the same dissipative solitons,and making the dissipative soliton cascade replication repeatable.Finally,we summarize this article and look forward to the future work in this field.