标题： 精确解和大地位势预报方程的自守系统 显示英文标题

标题： Exact solutions and automorphic systems of the geopotential forecast equation

摘要： 继续研究最近构建的大地测量势预报方程的群叶结构。 群叶结构包括两个系统，即自同构系统和求解系统，对其分析有助于原方程不变解的推导。 由于获得求解系统（甚至其在子群上的约简）的一般解存在问题，因此考虑其各种特解。 因此，出现了关于对应于通过其他方法获得的精确解的自同构系统特定形式的问题。 这在比较通过不同方法得到的解以及特定自同构系统的积分方面具有重要意义。 这个问题在多个示例中进行了讨论。 显示英文摘要

摘要： The study of the recently constructed group foliation for the geopotential forecast equation is continued. The group foliation consists of two systems, namely the automorphic and resolving systems, the analysis of which facilitates the derivation of invariant solutions for the original equation. As obtaining a general solution to the resolving system (even to its reductions on subgroups) is problematic, its various particular solutions are considered. Consequently, the question arises concerning the specific forms of automorphic systems that correspond to exact solutions obtained through alternative methods. This is of interest for both comparing solutions derived through different approaches and for the integration of specific automorphic systems. The problem is discussed in a number of examples.