Why it works better

The moving frame of reference formulation effectively transforms the Nagumo PDE from a reaction-diffusion equation to a reaction-diffusion-advection equation, i.e., in the moving frame of reference, the Nagumo equation can be written as an initial value problem
$$\begin{align*}\text{mPDE} & \quad & \frac{\partial \tilde{u}}{\partial t} & = \f... ...repsilon \sech (\beta z), & \quad & -\infty < z < \infty, \nonumber \end{align*}$$
with $\tilde{u}(z,t) = u(z+c_0 t,t).$Note that for c₀=4/3 and $\beta_0=2/3$ we have

$$\lim_{t \rightarrow \infty} \biggl\lvert \tilde{u}(z,t) - \frac{1}{1+Ke^{\beta_0 z}} \biggr \vert = 0,$$

that is, the non-constant ``standing wave'' solution to the reaction-diffusion-advection PDE to which the initial condition evolves is known analytically up to a shift constant K.