Stability of the fixed points of the complex Swift-Hohenberg equation

2015 International Conference on Mathematics, its Applications, and Mathematics Education

数学;教育

Khairudin, N.I.^1 ; Abdullah, F.A.^1 ; Hassan, Y.A.^1

School of Mathematical Sciences, Universiti Sains Malaysia, Penang

MY

11800, Malaysia^1

关键词: Dispersion parameters;    Euler-Lagrange equations;    Fixed points;    Imaginary axis;    Soliton-like solution;    Swift-hohenberg equations;    Trial functions;    Variational formulation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/693/1/012003/pdf
DOI  :  10.1088/1742-6596/693/1/012003

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

We performed an investigation of the stability of fixed points in the complex Swift- Hohenberg equation using a variational formulation. The analysis is based on fixed points Euler-Lagrange equations and analytically showed that the Jacobian eigenvalues touched the imaginary axis and in general, Hopf bifurcation arises. The eigenvalues undergo a stability criterion in order to have Hopf's stability. Trial functions and linear loss dispersion parameterare responsible for the existence of stable pulse solutions in this system. We study behavior of the stable soliton-like solutions as we vary a bifurcation .