of the initial condition at a later time. Both examples exhibit behavior typical of collisions of KdV solitons. In the first, one wave is significantly larger than the other, and completely subsumes it during the interaction. In the second, the waves have similar amplitude, with the trailing wave bumping into the leading wave and transferring energy without fully merging.

Despite these similarities, the amplitude of the waves in our examples are too large for the assumptions in the derivation of the KdV equation to hold. In particular, the larger wave in the first example is more than half the fluid depth in height, and there is significant vertical motion of the fluid when the waves pass by. A detailed comparison of the Euler and KdV equations for waves with these properties is carried out in §\[sec:kdv\]. A review of the literature on water wave collisions and the accuracy of the KdV model of water waves is also given in that section.

Rather than compute such solutions by increasing the amplitude from the linearized regime via numerical continuation, as was done for counter-propagating waves in [@water2], we use collisions of right-moving Stokes waves as starting guesses. The goal is to minimally 