If the waves did not interact, the combined solution would be time-periodic (to the extent that $5T_C=6T_A$, i.e. to about $0.076\%$). But the waves do interact. In addition to the complicated interaction that occurs when they collide, each slows the other down between collisions by introducing a negative gradient in the velocity potential between its own wave crests. Indeed, as shown in the right panel of Figure \[fig:AandC\], the velocity potential increases rapidly across a right-moving solitary wave and decreases elsewhere to achieve spatial periodicity. The decreasing velocity potential induces a background flow opposite to the direction of travel of the other wave. In the left panel of Figure \[fig:align:stokes\], we see that the net effect is that neither of the superposed waves has returned to its starting position at $t=5T_C$, and the smaller wave has experienced a greater net decrease in speed. However, as shown in the right panel, by adjusting the amplitude of the smaller wave (replacing solution C by B) and increasing $T$ slightly to $138.399$, we are able to hand-tune the Stokes waves to achieve $\tilde
f\approx5.5\times10^{-8}$, where $\theta$ is set to zero in (\[eq:f1\]). Note that as $t$ varies from 0 to $T/10$ in the 