正则化短脉冲与Ostrovsky方程的多脉冲存在性
Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations
摘要：
在可逆的、保守的、奇摄动的矢量场中，证明了单峰脉冲在轨道翻转分岔附近多脉冲解的存在性。与非奇异情况类似，包含第一积分的几何条件的符号决定是否存在多脉冲。证明利用几何奇异摄动理论和李雅普诺夫-施密特减少通过林的方法相结合。考虑奇异摄动系统中轨道翻转的动机来自正则化短脉冲方程和奥斯特洛夫斯基方程，它们都适合这个框架，并在这里显示为支持多脉冲。
英文摘要：
The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pulses exist or not. The proof utilizes a combination of geometric singular perturbation theory and Lyapunov--Schmidt reduction through Lin's method. The motivation for considering orbit flips in singularly perturbed systems comes from the regularized short-pulse equation and the Ostrovsky equation, which both fit into this framework and are shown here to support multi-pulses.
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