Modulational Stability of Envelope Soliton in a Quantum Electron-Ion Plasma in Three Dimension - A generalised Nonlinear Schr ̈odinger Equ ation in 3D

Modulational stability of envelope soliton is studied in a quantum dusty plasma in three dimension.
The Krylov-Bogoliubov-Mitropolsky method is applied to the three dimension plasma governing
equations. A generalised form of Nonlinear Schr¨odinger equation is obtained whose dispersive term
has a tensorial character. Stability condition is deduced abintio and the stability zones are plotted
as a function of plasma parameters