Page 48 - swp0000.dvi
P. 48
(20) (20) (20) (20) (20)
The coefficients of the harmonic modes 3 1 2 1 and 2
are given by
(20) 1
3 =
2
³ ´
(20) 0 2 (20) 3
1 = (2 + ) − 3
3
2 2
³ ´
(20)
2
2
2 = − 3 (20)
2
2
∙ 2 2 2 ¸
2
0 (2 0 + 0 +3 0 )
(20)
1 = ¡ 0 ¢ 2 2 2 − 3 (20)
2
0 − 3 0 ( 0 − 3 0 )
and
2 2 2
(20) ( 0 ) [ ( 0 +3 0 )+6 0 ]
= ¡ ¢
2
2 2
2
2
0 − 3 0 ( 0 − 3 0 )
0 (20)
−¡ ¢ 3
2
0 − 3 0
where
⎡ ⎤
3
0 0 0 2
2 − 2 + 3 (2 + )
2 2
⎢ ⎥
2
3 2
3
2
1 = − ⎣ ( 0 +3 0 +2 0 ) ⎦
+ 0
2
2 2
2
( 0 −3 0)( 0 −3 0 )
and
2 2
2
0 0 0 0
2 = +(1 − ) − − ¡ ¢
2
2 0 − 3 0
Finally, the first harmonic ( =1), of the third order perturbed quantities
gives the following NLS equation
(1) 2 (1)
¯ ¯ 2 (1)
1 + 1 + ¯ ¯ 1 =0 (2.16)
¯ (1)¯
1
2
The coefficient of dispersion term, is given by
36
