在本篇論文中，我們推導出修正版可壓縮流歐拉-泊桑方程的全域古典解所滿足的 Riccati 方程。在歐拉座標下的歐拉-泊桑方程所推導出的 Riemann 不變量方程，構成一個 2×2 的雙曲平衡律系統。利用廣義 Lax 變換，並對這個 2×2 的 Riemann 不變量系統進行微分，我們可以得到一組與 Riemann 不變量的空間導數相關的 2×2 Riccati 方程。;In this thesis， we derive the Riccati equations for the global classical solutions to the modified version of compressible Euler-Poisson equations. The equations for the Riemann invariants which will be derived from the Euler-Poisson equations in Eulerian coordinates， form a two-by-two hyperbolic system of balance laws. Using the generalized Lax transform， and differentiating the two-by-two system of Riemann invariants， we are able to obtain the two-by-two Riccati equations related to the spatial derivatives of the Riemann invariants.
