论文标题
严格验证了库拉莫托 - 西瓦辛斯基PDE中的HOPF分叉
Rigorous validation of a Hopf bifurcation in the Kuramoto-Sivashinsky PDE
论文作者
论文摘要
我们使用计算机辅助的证明技术来证明库拉莫托 - sivashinsky局部微分方程中的非平衡平衡解决方案的分支会经历HOPF分叉。此外，我们获得了霍普夫分叉附近时间周期解决方案家族的基本建设性证明。为此，在霍普夫点附近，我们在降低的配方中重写了库拉莫托 - 苏瓦辛斯基方程的时间周期性问题。然后，我们采用参数化的牛顿 - 坎多维奇方法来验证时间周期轨道的解决方案分支。通过构造，该解决方案分支包括HOPF分叉点。
We use computer-assisted proof techniques to prove that a branch of non-trivial equilibrium solutions in the Kuramoto-Sivashinsky partial differential equation undergoes a Hopf bifurcation. Furthermore, we obtain an essentially constructive proof of the family of time-periodic solutions near the Hopf bifurcation. To this end, near the Hopf point we rewrite the time periodic problem for the Kuramoto-Sivashinsky equation in a desingularized formulation. We then apply a parametrized Newton-Kantorovich approach to validate a solution branch of time-periodic orbits. By construction, this solution branch includes the Hopf bifurcation point.
