Page 44 - swp0000.dvi

2
 = ( −   )   =  

and thus

   2    
→ −    +   → +   (2.5)
      
where  is a small (real) parameter and   is the envelope group velocity

to be determined later. The dependent variables are expanded as:

∞ 
X X
A( )= A 0 +   A () ( )exp (Θ)  (2.6)

=1 =−
where

h i 
() () () () () ()
A  
 =             
A (0) =[ 0  0 0 0 0]  and Θ =  − ,


where  and  are real variables representing the fundamental (carrier)

()
wavenumber and frequency, respectively. All elements of  satisfy the

reality condition  () =  ∗() , where the asterisk denotes the complex con-

−
jugate and   stands for the transpose. Substituting equations (2.5) and
(2.6) into equations (2.1)-(2.4) and collecting terms of the same powers of

,the first-order ( =1)equations with  =1,gives

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