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Then (6.101) and (6.102) become
sin j π
i ν 2 c
j ) w
w 0
2 (1
cos j π
e j ( w )= a j
at
j =2 k +1 ,
(6.108)
j ) w
w 0
2 (1
cos j π
i ν 2 c
j ) w
w 0
2 (1
sin j π
e j ( w )= a j
at
j =2 k.
(6.109)
j ) w
w 0
2 (1
The coecients a j are determined from the normalization condition (6.107)
and are given by
iΩ
(2 w 0 ) 1 / 2 .
a j =
(6.110)
Substitution of numerical values of parameters in (6.110) yields
a j = i 1 . 59
n 1 / e L 3 (2 w 0 ) 1 / 2 .
The coecient C 0 j is obtained from (6.97). With normalization condition
(6.107), we have at p =6
2 c 2 w 0
2 dln ω j
d ν
I 1
πL 2 R E ,
1) j +1 m 2 a j
C 0 j =(
(6.111)
where
π
cos ( j (1
j ) t
1+3 w 0 t 2 2
I 1 =
d t.
0
Then
10 8 m 2
dln ω j
d ν
1) j +1 2
×
C 0 j =(
I 1 .
For calculation of the wave field we use lengths in kilometers. After the nor-
malization we have
L C 0 j = 2 m 2 ( L
1) 1 / 2
1) j +1 10 4 ( L
1) 1 / 2
dln ω j
d L
I 1 (km 1 ) .
C 0 j =(
R E
Introduce the coecient of excitation of the j -mode as
e j = n j e j .
 
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