驻波广义Fisher-Kolmogorov方程的广义同宿轨

研究驻波广义Fisher-Kolmogorov方程u″″-βu″+u~3-u=0,β0.该方程有一个鞍中心型平衡点u=0(一对非零实特征值和一对纯虚特征值).应用扰动理论和调整相移,证明对每一个正常数β该方程在原点附近有一个连接周期解的同宿轨(该文称为广义同宿轨).

Generalized Homoclinic Solutions for the Stationary ExtendedFisher-Kolmogorov Equation

This paper investigates the stationary extended Fisher-Kolmogorov equation u'-βu'+ u³-u=0,  β>0, which has a saddle-center equilibrium u = 0 (two nonzero real and two nonzero imaginary eigenvalues). Applying a perturbation method and adjusting some phase shift constants, we prove that it has a homoclinic solution connecting a periodic solution (called generalized homoclinic solution, thereafter) near the origin for each positive constant β.