We are thinking of EMT/MET transition.
With certain modelling,
https://hal.science/hal-02520861v2/document
When we want traveling wave solution with asymptotic states, we take some function depenedent on (x - ct), where x is the position, and t is time, and c is the speed of propageting front.
But, numerically it is difficult to calculate the speed. so we approximate by comparing the previous time function and current time function.
Comment. Now I am interested in the rigorous proof of the existence of traveling wave.