  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 P\'olya.
