Ogt lvte 
The transform of the right-hand side of Equation (5) can be computed 
as follows 
ie,9) 2 2 os) i 
we ‘ ze 
fos e ify ——- = ih dye ve [log (y-iH) + log (y+iH) - 
-0O 
a ‘ - 2 log l 
co 
l . -ily Le AO 6 xo stleghe 
yf ke Vea yas my 
- 00 
a ee e -HILl] 
The integral term in Equation (5) can be treated as an ordinary con- 
volution integral, with the result that 
asit ¥ ody Py Mache 
pr ef ee 
—so - oO 
- ae [ily* (x :L)] [wi sgn L | = K|L|¥* (x ;L) 
The integro-differential equation now becomes an ordinary differen- 
tial equation with respect to x 
vt (x sf) + Kilt sf) = Pi peti aie 
The solution of this equation is now readily obtained. A par- 
ticular solution is the following 
Tr . - nly 1 - cos K| | ; 
=" ipa P.O) (by Equation (2) ) . 
v(x 32) 
(7) 
In principle, we should include the complementary solution, and this 
would be easy enough to do. However, the above solution appears to 
suffice for all that follows. 
1496 
