Kinetic envelope soliton in non-thermal quantum pair-ion plasma and Wigner stability

Using Wigner-Moyal formulation for the pair-ion plasma, with the residual electrons present we have derived the nonlinear Schrodinger equation for the kinetic envelope soliton with the help of Krylov-Bogoliubov-Mitropolsky approach. This is a full-quantum mechanical treatment of the problem where all the species (both ion and electrons) are treated on the same footing. The stability property of the nonlinear Schrodinger equation is then analyzed with the help of Wigner-transform in phase space. Our approach has the advantage that one can study the stability for various form of initial spectral distribution. The standard modulational stability is a special case of this approach. The experimental observation of the temperature difference between the species in pair ion is taken care of by the Cairns non-thermal distribution. It is observed that non-thermality has a good influence on the propagation characteristics and on the stability properties.