标题： 第一 Painlevé 层级的无极解以及 KdV 方程的非一般临界行为 显示英文标题

标题： Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation

摘要： 我们建立了Painlevé I层次中所有偶数成员的实无极点解的存在性。 我们还获得了这些解的渐近行为，并描述了它们在小色散极限下KdV方程解的临界渐近行为中的相关性。 在一般临界点的情况下已经理解了这一点，我们在此将其推广到非一般临界点的情况。 显示英文摘要

摘要： We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the description of critical asymptotic behavior of solutions to the KdV equation in the small dispersion limit. This was understood in the case of a generic critical point, and we generalize it here to the case of non-generic critical points.