On the zeros of the Pearcey integral and a Rayleigh-type equation

Abstract

In this work we find a sequence of functions at which the Pearcey function is identically zero. The sequence of functions can be expressed in terms of a second order non-linear ODE, which happens to be the Rayleigh-type. As a byproduct of these facts, we develop a methodology to find a class of functions which solve the moving boundary problem of the heat equation. To this end, we make use of generalized Airy functions, which in some particular cases fall within the category of functions with infinitely many real zeros, studied by Pólya.

References in corpus (5)

• The Pearcey Process
• The Higher-Order Heat-Type Equations via signed Lévy stable and generalized Airy functions
• The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation
• On hitting times, Bessel bridges, and Schrodinger's equation
• On Schrödinger's equation, 3-dimensional Bessel bridges, and passage time problems