In this paper we have made use of reductive perturbation technique (RPT) and carried out homotopy analysis method (HAM) to investigate the effect of exchange correlation and quantum diffraction on the electrostatic waves in quantum magnetoplasma. We have derived a nonlinear Schrödinger equation (NLSE) by using RPT that describes the spatiotemporal evolution of an initial waveform. Apart from this technique, we have made use of HAM to second our initial findings. It has been shown that both quantum diffraction H and parameter streaming velocity \(u_0\) have significant effects in determining the stability criteria and the growth or decay of any instability created therein. The stable parametric regimes are crucial from the experimental point of view as well.

本文我们利用还原摄动技术（RPT）并进行了同伦分析方法（HAM），研究了交换相关性和量子衍射对量子磁等离子体中静电波的影响。通过使用描述初始波形的时空演化的RPT，我们已经推导出了非线性Schrödinger方程（NLSE）。除此技术外，我们还利用HAM来支持我们的最初发现。已经表明，量子衍射H和参数流速度\（u_0 \）在确定稳定性标准以及其中产生的任何不稳定性的增长或衰减方面都具有显著作用。从实验的角度来看，稳定的参数体系也至关重要。