  Stability of travelling waves for the Nagumo equation on the whole line is
proven using a new approach via functional inequalities and an implicitely
defined phase adaption. The approach can be carried over to obtain pathwise
stability of travelling wave solutions in the case of the stochastic Nagumo
equation as well. The noise term considered is of multiplicative type with
variance proportional to the distance of the solution to the orbit of the
travelling wave solutions.
