TITLE:
Pulsating Solitons in the Two-Dimensional Complex Swift-Hohenberg Equation
AUTHORS:
Aladji Kamagaté, Alain-Brice Moubissi
KEYWORDS:
Pulsating Solution, Dissipative Soliton, Spatio-Temporal, Collective Coordinate Approach, Ginzburg-Landau Equation, Complex Swift-Hohenberg Equation, Spectral Filtering, Bifurcation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.10,
October
29,
2018
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.