We study the phenomenon of revivals for the linear Schrödinger and Airy equations over a finite interval, by considering several types of non-periodic boundary conditions. In contrast to the case of the linear Schrödinger equation examined recently (which we develop further), we prove that, remarkably, the Airy equation does not generally exhibit revivals even for boundary conditions very close to periodic. We also describe a new, weaker form of revival phenomena, present in the case of certain Robin-type boundary conditions for the linear Schrödinger equation. In this weak revival, the dichotomy between the behaviour of the solution at rational and irrational times persists, but in contrast to the classical periodic case, the solution is not given by a finite superposition of copies of the initial condition.

我们通过考虑几种类型的非周期性边界条件来研究有限区间内线性薛定谔方程和艾里方程的复活现象。与最近检查的线性薛定谔方程的情况（我们进一步发展）相比，我们证明，值得注意的是，即使对于非常接近周期性的边界条件，艾里方程通常也不会重现。我们还描述了一种新的、较弱的复活现象形式，存在于线性薛定谔方程的某些罗宾型边界条件的情况下。在这种弱复兴中，有理时间和无理时间解的行为之间的二分法仍然存在，但与经典周期情况相反，解不是由初始条件的副本的有限叠加给出的。