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Abstract
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In this work we study the modulational instability of plasmas with q-entropy electrons and warm ions,
using the hydrodynamic approach. A nonlinear Schrödinger equation (NLSE), governing the dynamics
of envelope excitations in the plasma, is obtained by using the conventional multiscales method.
Investigation of the modulational instability of the nonextensive plasmas reveals that the criteria for
propagation of bright/dark envelope excitations in such plasmas are significantly affected by value of
the nonextensivity parameter, q, and the fractional ion-temperature, σ. In particular, by setting σ = 0,
a new region of modulational instability appears, indicating that the study of modulation instability in
the cold-ion limit (σ = 0) is completely different from that of warm ions. The study of the growth-rate
and rogue-wave amplitudes in terms of different plasma parameters, reveals that their magnitude is of
different scales for two ranges of the nonextensivity parameters, q > 1 and q < 1.
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