Abstract
A formalism for nonlinear interaction of degenerate upper-hybrid waves (DUHWs) with degenerate ion-cyclotron waves (DICWs) and degenerate Alfven waves (DAWs) is revisited to account for quantum corrections owing to quantum Bohm potential, quantum exchange-correlations, and quantum statistical pressure. For this purpose, different nonlinear dispersion relations are derived with quantum settings. By using the phasor matching techniques, the growth rates of three wave decay and modulational instabilities are analyzed by identifying the nonlinear coupling of high-frequency DUHWs with low-frequency DICWs and DAWs. Numerically, it is revealed that parametric three wave decay and modulational instabilities are significantly influenced by the impact of Fermi pressure and exchange-correlation in a degenerate magnetoplasma. The present results are important to understand the dispersive properties of nonlinear waves and their mutual couplings at quantum scales in degenerate environments like white dwarfs, neutron stars, and magnetars.
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