Falttnsen 
zero at a proper later point. This equation system does give waves. 
The solution to the equation system with z, = 0 can be found 
in Ogilvie & Tuck (1969). It is 
i = 
% 1 (xy, 2, t) = = 5 oe og: ee eae F {o (x) e : Cee 
(59) 
H—0 1 
eo Ee ara 3 UR ee 
where 
-l vx -ikx -ivx 
F \o (x) e } = dsc. ve a(x) e 
—-Sso 
= le oc clade Ua 
We will rewrite (59) ina way similar to the way we did 
with (15) in the zero-speed problem. See Appendix C for more 
details. 
We can write 
oy Gry ast) =" Bix, y. 2) te (60) 
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