JAMP  Vol.6 No.10 , October 2018
Pulsating Solitons in the Two-Dimensional Complex Swift-Hohenberg Equation
Abstract: 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.
Cite this paper: Kamagaté, A. , Moubissi, A. (2018) Pulsating Solitons in the Two-Dimensional Complex Swift-Hohenberg Equation. Journal of Applied Mathematics and Physics, 6, 2127-2141. doi: 10.4236/jamp.2018.610179.

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