1. Note that ϕ is not a meromorphic function even if ψ is.
2. This problem anticipates some of the discussions of Section 11.
3. The standard reference on water waves is Stoker (1957).
4. A lucid exposition may be found in Curle & Davies (1968), Ch. 21.
5. This follows because in this case when (α±β) ≃ 0.