Page 90 - swp0000.dvi

The system neutrality condition is given by

 0 =  0 +    0 +    0  (4.3)

where   and   are the charge numbers of negatively charged hot and

cold dust, respectively.

4.2 Nonlinear Analysis

To discuss the electrostatic dust acoustic wave properties, we use the

reductive perturbation technique [150]. The independent variables are
stretched as [151, 152]

 =  12 ( − )  Θ =  −12   =  and  =  32  (4.4)

where  is a small real parameter and  is the wave propagation speed. All

dependent variables in this model are expanded as:

2 (2)
  =  0 +  (1) +    + 

(1) 2 (2)
  =   +    + 
(1) 2 (2)
  =  0 +  +   + 
 


  =  32 (1) +  52 (2) + 
 
(1)
  =  32   +  52  (2) + 

2 (2)
 =  (1) +   +  (4.5)

where     and   are the cold and hot velocities in  Θ and 
directions, respectively. Employing the stretching variable (4.4) and the

expansions (4.5) in equations (4.1)-(4.2), the neutrality condition is given

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