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tion in medium with dispersion properties exhibits amplitude modulation
caused by medium nonlinearity and carrier wave self-interaction. Later, ef-
fects of plasma parameters on acoustic wave modulation stability in warm
plasma have been studied by Chawla et al.[134]. They found that, the in-
stability regions are shifted with the wave number. On the other hand, the
conditions for instability regions and rational solution of the NLS equation
have been obtained in auroral zone plasma [135]. Nonlinear modulation
electrostatic and electromagnetic wave packets in laboratory and astro-
physics have been discussed [143]. Our aim in the present chapter is to
study the MI of a two-temperature dusty plasma with nonthermal elec-
trons, and inspecting the dark and bright envelope solitons.
3.2 Modulational Instability
We examine the effects of plasma parameters of the system (2.1-2.5),
model presented in chapter 2, such as ion nonthermality, hot and cold
dust temperatures (charges) on MI and the envelope soliton formation, via
equation (2.16); namely
2
2
+ + || =0 (3.1)
2
(1)
where ≡ for simplicity. The dispersion coefficient and the coeffi-
1
cient of the nonlinear term, (replaced by in the following text), are
given by equation (2.18) and (2.19) respectively
For stability analysis of amplitude modulation of DAWs, we set
£ 2 ¤
=[ + ()] exp − | | (3.2)
0
0
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