Figure 13.

Applying the proposed scheme in the case of two different pulse lengths; ${\tilde{\tau }}_{\mathrm{b}}=0.2$ (left) and ${\tilde{\tau }}_{\mathrm{b}}=0.04$ (right). The dimensionless space and time steps are $\Delta \tilde{x}=\Delta \tilde{t}=0.01$. This time step is actually not much smaller than the shorter pulse length, so, for example, the tips cannot be plotted accurately when ${\tilde{\tau }}_{\mathrm{b}}=0.04$, but the solution still performs well.