KBM approach to dust acoustic envelope soliton in strongly coupled plasma

Evolution of dust acoustic envelope soliton is analyzed in a strongly coupled plasma where electrons and ions are assumed to be Maxwellian distributed. The dynamics of unmagnetized plasma is described by the fluid equations. A multiscale perturbation analysis based on Kyrlov-Bogoliubov-Mitropolsky method is carried out, along with the assumption that strong coupling between the dust particles is described by the electrostatic temperature of Yaroshenko et al. This model of a strongly coupled dusty plasma is based on effective electrostatic temperature which is a function of the potential and density and as such also a dynamically varying quantity and also requires a perturbation. In our KBM approach we require all these upto third order of scaling parameter. Since uptill now all the papers contain only second order expansion of this effective temperature. We have given the details of third order expansion in an appendix. After the derivation of the Nonlinear Schrodinger Equation we have analyzed the modutational instability for various values the plasma parameters and the strength of the strong coupling. Our main intention is to analyze the effect of strong coupling on dusty-envelope soliton.