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| Symplectic conservative integration for short-wave approximation |
| Revised:August 26, 2005 |
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| DOI：10.7511/jslx20081004 |
| KeyWord:symplectic conservation,coordinate canonical transformation,mixed energy density,WKBJ approximation |
| ZHONG Wan-xie SUN Yan |
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| Abstract: |
| All approximations for a conservative system should be symplectic conservative.The traditional perturbation approaches are based on the Taylor series expansion which uses additional operation.The addition for a transfer symplectic matrix is not symplectic conserved,however,the symplectic matrices are conserved under multiplication.The symplectic conservative perturbation for a conservative system can use the canonical transformation method.However,the well-known WKBJ short wave-length approximation is not symplectic conservative.The former paper[7] has not taken the coordinate transformation into consideration,more steps of integration are necessary.The method of coordinate transformation and the polynomial approximation of mixed energy density are applied in this paper,and then the solution of unknown state vector is solved,which needs far fewer steps of integration.Numerical results demonstrate the effectiveness of the present method. |
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