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| Is the WKBJ approximation symplectic conservative? |
| Revised:December 01, 2004 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20051002 |
| KeyWord:WKBJ approximation,conservative system,symplectic conservation,canonical (transforma-)tion |
| ZHONG Wan-xie~*,GAO Qiangt,Dalian University of Technology,Dalian 116024,China) |
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| Abstract: |
| 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. |
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