WKBJ近似保辛吗?

WKBJ短波近似是最常用的有效求解方法之一。保守体系的微分方程可用Hamilton体系的方法描述，其特点是保辛。保辛给出保守体系结构最重要的特性。但WKBJ短波近似却未曾考虑保辛的问题。本文给出验证近似解保辛的条件，并指出WKBJ近似难于保辛。然后给出正则变换的摄动保辛方法。数值例题展示了提出的保辛算法的有效性。

Is the WKBJ approximation symplectic conservative?

The well-known WKBJ short wave length approximation is one of the popularly applied approaches for the solution of differential equations. The differential equation of a conservative system can be described by means of the Hamilton system theory, for which the key characteristic is symplectic conservation, one of the most important features of a conservative system. However, the WKBJ approximation has not taken the symplectic conservation into consideration. The present paper presents the symplectic conservative condition for an approximate solution and then describes that the WKBJ approximate solution cannot ensure symplectic conservation. The canonical transformation method is proposed for symplectic conservative perturbation approximation. Numerical examples demonstrate the effectiveness of the proposed symplectic conservative algorithms.