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This study investigates the modulation instability of magnetosonic waves in a semiconducting quantum plasma system. Utilizing the quantum hydrodynamic model, we derive the nonlinear Schrödinger equation and its solution through the reductive perturbation technique. The growth rate of modulation instability for magnetosonic waves has been derived. This study incorporates various quantum corrections, including Fermi degenerate pressure, exchange-correlation potential, and Bohm potential. We study the bright soliton profiles of magnetosonic waves, and additionally, we conduct graphical analyses of the linear dispersion relation and the product of the dispersive coefficient (P) and nonlinear coefficient (Q) of the nonlinear Schrödinger equation. It has been found that magnetosonic waves exhibit modulation instability within specific parameter ranges of the semiconductor plasma and at certain wavelength regimes. Further, we present a comparative study between GaSb and InSb semiconducting plasma systems. The exchange-correlation potential and Fermi degenerate pressure have significantly impacted the modulation instability growth rate, whereas the effect of the Bohm potential is much lower.
Sharma et al. (Mon,) studied this question.