The nonlinear coupling of high-frequency upper-hybrid (UH) pump waves with low-frequency lower-hybrid (LH) waves is studied in a degenerate magnetoplasma, comprising of quantum electrons and classical ions. For this purpose, the framework of quantum hydrodynamic model is utilized to examine the Fermi pressure effects on the nonlinear dispersion relations of UH and LH waves with quantum settings. Furthermore, by applying the Fourier analysis and collecting the same phasor terms, the nonlinear dispersion relations can be coupled to investigate the growth rates of three-wave decay and modulational instabilities under certain approximations. It is noticed that inclusion of electron Fermi pressure significantly alters the parametric three-wave decay and modulational instabilities besides the corrections due to quantum exchange-correlations and Bohm potential in degenerate magnetoplasmas. The present findings might be useful to understand the nonlinear wave interactions in superdense astrophysical environments, e.g., white dwarfs, magnetars, neutron stars, etc.

在由量子电子和经典离子组成的简并磁等离子体中研究了高频上混合泵浦波与低频下混合波的非线性耦合。为此，利用量子流体动力学模型的框架来研究费米压力对具有量子设置的UH和LH波的非线性色散关系的影响。此外，通过应用傅立叶分析并收集相同的相量项，可以将非线性色散关系耦合以研究在某些近似下的三波衰减和调制不稳定性的增长率。注意到，除了归因于简并磁等离子体中的量子交换相关性和玻姆势的校正之外，包含电子费米压力还显着改变了参数三波衰减和调制不稳定性。目前的发现可能有助于理解超矮天体环境中的非线性波相互作用，例如白矮星，磁星，中子星等。