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where  () are dispersion (nonlinear) coefficients. Equation (1.11) de-

scribes a slowly varying wave propagating in a weakly nonlinear, strong

dispersive or inhomogeneous media. It is noted that, envelope solitary
wave pattern is obtained from a generalized NLS equation [24]. For wave

packets progress in dispersive medium, the slow variation in wave packets

envelope due to the nonlinear effects and modulational instability (MI)

may be obtained. El Wakil et al [25] investigated the envelope solitary
waves in plasmas with nonthermal electrons. Also, many authors in-

spected modulation instability of acoustic waves in plasmas with different

non-Maxwellian velocity distribution.

1.6 Acoustic Waves in Plasmas

According to wave frequencies range, disturbances on sun, magne-

tospheres, stars, solar wind and ionosphere generate propagating waves

[26]. The electrostatic waves in dispersive media will be generated when

the perturbation creates charge imbalance in the neutral fluid elements.
This will accelerate charged particles in neighborhood of charged fluid

resulting in charges oscillating back-forth. These oscillations occur for

electric field only and defined as electrostatic waves (no oscillation for

magnetic field).
In electromagnetic waves, both oscillating electric and magnetic field

components are present. Examples of these waves are Alfvén and magne-

tosonic ion waves.

1.6.1 Ion Acoustic Waves (IAWs)

Ion acoustic soliton propagation is one of the very important non-
linear waves in plasma fluids. It has been investigated both experimen-

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