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轴对称磁静平衡态被广泛用来描述不同尺度的恒星大气结构。对这类平衡态,可引入所谓磁通量函数来描述磁场,它满足一变系数、非线性椭圆型方程。迄今为止,人们只就线性情况的某些特例给出该方程的解析解;对较为复杂的情况,特别是非线性情况,还未找到有效的办法进行解析处理。本文将应用微变换方法求上述变系数、非线性方程的相似解,并给出普遍结果。有关特解的具体形式及对太阳大气的应用将在本系列的下几篇论文中另作讨论。
Axisymmetric magnetostatic equilibrium is widely used to describe the structure of stellar atmospheres at different scales. For such equilibrium states, a so-called flux function can be introduced to describe the magnetic field, which satisfies a variable coefficient, nonlinear elliptic equation. So far, the analytical solution of this equation has been given only for some special cases of linearity. For more complicated cases, especially for non-linear cases, no effective solution has yet been found. In this paper, we will use the method of micro-transformation to find the similar solutions of the above-mentioned variable coefficients and nonlinear equations and give the general results. The specific forms of solutions and their application to the solar atmosphere will be discussed separately in the next few articles in this series.