| 一个有关KdV方程的不变性 |
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| 引用本文： | 南志杰,余立海. 一个有关KdV方程的不变性[J]. 嘉兴学院学报, 2011, 23(6): 21-24. DOI: 10.3969/i.issn.1008-6781.2011.06.004 |
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| 作者姓名： | 南志杰 余立海 |
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| 作者单位： | 嘉兴学院数理与信息工程学院,浙江嘉兴,314001 |
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| 摘 要： | 通过对KdV方程的Backlund变换的分析，将其改造成一个Ricatti系统，并求解此系统，以此为基础，利用“不变性求解法”研究KdV方程的一类解的递推公式，从而由KdV方程的一对显然解出发计算出了它的更复杂的精确解．
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| 关 键 词： | KdV方程 Baicklund变换 不变性 精确解 Ricatti系统 |
Invariance of the KdV Equation |
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| NAN Zhi-jie,YU Li-hai. Invariance of the KdV Equation[J]. Journal of Jiaxing College, 2011, 23(6): 21-24. DOI: 10.3969/i.issn.1008-6781.2011.06.004 |
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| Authors: | NAN Zhi-jie YU Li-hai |
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| Affiliation: | NAN Zhi-jie,YU Li-hai(School of Mathematics,Physics and Information Engineering,Jiaxing University,Jiaxing,Zhejiang 314001) |
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| Abstract: | An analysis of Backlund transformation for the KdV equation is made, and then the KdV equation is transformed into a Ricatti system. And based on the solution to the system, by usingthe＂invariant＇ method＂, a recursive formula of solution to the KdV equation is studied. Accordingly, from a pair of the evident solutions to the KdV equation, its more complex and accurate solutions could be computed. |
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| Keywords: | KdV equation Backlund transformation invariance accurate solution Ricatti System |
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