Page 46 - swp0000.dvi
P. 46
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(2) 2 2 (1) 2 2
0 (3 0 − 0 )+ 1 ( − )( 0 +3 0 )
1
(2)
=
2
2
1 ( 0 − 3 0 ) 2
(2.12)
The compatibility condition gives
5
2
2
2
2
2
2
2
4 3 − ( − 4 0 )( 0 − 3 0 ) 2
= = 0 (2.13)
3
2
2
4
2
2
2
2
4 ( 0 ( 0 − 3 0 ) + )
0
The compatibility condition (2.13) is just the group velocity of the
envelope soliton.
The second harmonic modes ( =2) of the second order perturbed
quantities, arising from the nonlinear self-interaction of the carrier waves,
h i 2
are obtained in terms of (1) as
1
h i 2
(2) = (22) (1)
2 1 1
h i 2
(2) = (22) (1)
2 2 1
h i 2
(2) = (22) (1)
2 1 1
h i 2
(2) (22) (1)
=
2 2 1
h i 2
(2) = ∆ (1) (2.14)
1
2
(22)
where ( =1 and 2) and the coefficients of the harmonic modes
(22) (22) (22) (22)
1 2 1 and 2 are given by
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