Let f(x, y, z, t) satisfy the equation
For certain purposes, particularly in connection with the propagation of a boundary of fusion etc., it is of interest to discover solutions of (1) which permit the equation:
to be solved explicitly in the form:
This suggests the examination of solutions of the type
where
and f, ϕ, ψ are functions to be determined. To save repetition, Roman capitals denote arbitrary constants throughout.