By introducing the Kappa distribution function ($\kappa$) and considering the dimensionless variables and applying them to the Poisson equation, the Bohm sheath equation in a plasma is obtained. We know the above distribution function has two important factors: 1-the invariant kappa spectral index (${\kappa }_0$), 2-the number of degrees of freedom ($d_{e,\mathrm{\Phi }}$). In this regard, we considered soliton with positive and negative potentials in the two areas of the solar structure Heliosphere (positive potential: near equilibrium areas ${\kappa }_0>1$ and negative potential Heliosheath: out of equilibrium areas $0<{\kappa }_0<1$). Then, the Korteweg-de-Vries equation (KdV) is obtained using the Bohm criterion and applying the Sagdeev pseudo potential method and effects of the spectral index ${\kappa }_0$, the potential degrees of freedom $d_{e,\mathrm{\Phi }}$ via perturbation are studied numerically.

通过引入 Kappa 分布函数（$\kappa$) 并考虑无量纲变量并将它们应用于泊松方程，得到等离子体中的玻姆鞘方程。我们知道上面的分布函数有两个重要的因素：1-不变的kappa谱指数（${\kappa }_0$), 2-自由度数 ($d_{\mathrm{电子},\mathrm{\Phi }}$）。在这方面，我们考虑了太阳结构日光层两个区域中具有正负电位的孤子（正电位：接近平衡区域${\kappa }_0>1$ 和负电位 Heliosheath：超出平衡区域 $0<{\kappa }_0<1$）。然后，使用 Bohm 准则并应用 Sagdeev 伪电位方法和光谱指数的影响，获得 Korteweg-de-Vries 方程 (KdV)${\kappa }_0$, 潜在的自由度 $d_{\mathrm{电子},\mathrm{\Phi }}$ 通过扰动进行数值研究。