A Shooting Approach to Layers and Chaos in a Forced Duffing Equation
A Shooting Approach to Layers and Chaos in a Forced Duffing Equation
复制标题
强迫达芬方程中的层和混沌的射击方法
DOI：
10.1006/jdeq.2002.4166
复制
发表时间：
2001
影响因子：
2.4
通讯作者：
S. Hastings
中科院分区：
文献类型：
--
作者：
S. Ai;S. Hastings
研究了ut = e2u xx−u 3 +λu+cos x, u x (0, t)=u x (1, t)=0问题的平衡解。我们用射法求出了所有非零e的解。对于小e，我们将前人的解，特别是Angenent、Mallet-Paret和Peletier、Hale和Sakamoto的解相加，并给出了新的初等ode证明。在新的结果中，存在内部层型解。考虑均衡满足的编码，但在无限区间上，我们获得了λ小于或等于3 2 2/3和0 1 / 4的混沌结果。我们还考虑了当λ增加时解的分岔问题。
Abstract We study equilibrium solutions for the problem u t =e 2 u xx −u 3 +λu+cos x, u x (0, t)=u x (1, t)=0. Using a shooting method we find solutions for all nonzero e. For small e we add to the solutions found by previous authors, especially Angenent, Mallet-Paret and Peletier, and Hale and Sakamoto, and also give new elementary ode proofs of their results. Among the new results is the existence of internal layer-type solutions. Considering the ode satisfied by equilibria, but on an infinite interval, we obtain chaos results for λ⩾λ 0 = 3 2 2/3 and 0 1 4 . We also consider the problem of bifurcation of solutions as λ increases.