In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating so...In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating soliton and fronts can be realised through a series of period-doubling bifurcations, while there exist many kinds of special solutions. The complete transformation diagram has been obtained when the value of nonlinear gain varies within a definite range. The detailed analysis of the diagram reveals that the pulsating soliton experiences period-doubling bifurcations for smaller values of the nonlinear gain. For larger values of it, the pulsating solitons show chaotic behaviour and complex pulse splitting except for some special bifurcations. With the value of nonlinear gain increasing further, the pulse profiles resume pulsating, but the pulse energy are much higher than before and the pulse centre may move along the propagation direction.展开更多
A semi-analytical approach for the pulsating solutions of the 3D complex Cubic-quintic Ginzburg-Landau Equation (CGLE) is presented in this article. A collective variable approach is used to obtain a system of variati...A semi-analytical approach for the pulsating solutions of the 3D complex Cubic-quintic Ginzburg-Landau Equation (CGLE) is presented in this article. A collective variable approach is used to obtain a system of variational equations which give the evolution of the light pulses parameters as a function of the propagation distance. The collective coordinate approach is incomparably faster than the direct numerical simulation of the propagation equation. This allows us to obtain, efficiently, a global mapping of the 3D pulsating soliton. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics.展开更多
In this paper, we performed an investigation of the dissipative solitons of the two-dimensional (2D) Complex Swift-Hohenberg equation (CSHE). Stationary to pulsating soliton bifurcation analysis of the 2D CSHE is disp...In this paper, we performed an investigation of the dissipative solitons of the two-dimensional (2D) Complex Swift-Hohenberg equation (CSHE). Stationary to pulsating soliton bifurcation analysis of the 2D CSHE is displayed. The approach is based on the semi-analytical method of collective coordinate approach. This method is constructed on a reduction from an infinite-dimensional dynamical dissipative system to a finite-dimensional model. The reduced model helps to obtain approximately the boundaries between the stationary and pulsating solutions. We analyzed the dynamics and characteristics of the pulsating solitons. Then we obtained the bifurcation diagram for a definite range of the saturation of the Kerr nonlinearity values. This diagram reveals the effect of the saturation of the Kerr nonlinearity on the period pulsations. The results show that when the parameter of the saturation of the Kerr nonlinearity increases, one period pulsating soliton solution bifurcates to double period pulsations.展开更多
文摘In this paper, a set of detailed numerical simulations of pulsating solitons in certain regions, where the pulsating solitons exist, have been carried out. The results show that the transformation between pulsating soliton and fronts can be realised through a series of period-doubling bifurcations, while there exist many kinds of special solutions. The complete transformation diagram has been obtained when the value of nonlinear gain varies within a definite range. The detailed analysis of the diagram reveals that the pulsating soliton experiences period-doubling bifurcations for smaller values of the nonlinear gain. For larger values of it, the pulsating solitons show chaotic behaviour and complex pulse splitting except for some special bifurcations. With the value of nonlinear gain increasing further, the pulse profiles resume pulsating, but the pulse energy are much higher than before and the pulse centre may move along the propagation direction.
文摘A semi-analytical approach for the pulsating solutions of the 3D complex Cubic-quintic Ginzburg-Landau Equation (CGLE) is presented in this article. A collective variable approach is used to obtain a system of variational equations which give the evolution of the light pulses parameters as a function of the propagation distance. The collective coordinate approach is incomparably faster than the direct numerical simulation of the propagation equation. This allows us to obtain, efficiently, a global mapping of the 3D pulsating soliton. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics.
文摘In this paper, we performed an investigation of the dissipative solitons of the two-dimensional (2D) Complex Swift-Hohenberg equation (CSHE). Stationary to pulsating soliton bifurcation analysis of the 2D CSHE is displayed. The approach is based on the semi-analytical method of collective coordinate approach. This method is constructed on a reduction from an infinite-dimensional dynamical dissipative system to a finite-dimensional model. The reduced model helps to obtain approximately the boundaries between the stationary and pulsating solutions. We analyzed the dynamics and characteristics of the pulsating solitons. Then we obtained the bifurcation diagram for a definite range of the saturation of the Kerr nonlinearity values. This diagram reveals the effect of the saturation of the Kerr nonlinearity on the period pulsations. The results show that when the parameter of the saturation of the Kerr nonlinearity increases, one period pulsating soliton solution bifurcates to double period pulsations.
