Abstract: Under the global climate warming condition, the dusty plasma diffusing phenomenon may bring a huge havoc. In this paper a class of generalized nonlinear solitary wave model of atmosphere dusty plasma diffusion was considered. Firstly, at typical non-disturbed situation, the analytic expression of solitary wave solution was obtained by using the undetermined coefficient method. Then from the method of generalized variation iteration, the variation multiplier was solved and the generalized variation iteration was constructed. Then we found out various iteration solutions of solitary waves. Further, the solitary wave of corresponding model for generalized nonlinear dusty plasma was obtained using a transform of travelling waves. Finally, from the homologous variation theory for the function sequence of obtained approximate solution, it is an uniformly convergent sequence on the corresponding argument area. Thus the limiting function from iteration solutions is the exact solution to the low frequency vibrated nonlinear equation for dusty plasma and the corresponding approximate solution is an approximate analytic solution. It can be further obtained dependent physical behaviors by using the analytic operation. For example, from the obtained peak value of the soliton wave, as corresponding measures, it avoid arises super-high density assemble physical behaviors of cause electric discharge spark-over phenomenon.

Key words: dusty plasma, variational iteration, approximate solution