| 基于Bell多项式求解非线性发展方程Hirota双线性形式的新算法 |
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| 引用本文： | 杨云青,陈勇. 基于Bell多项式求解非线性发展方程Hirota双线性形式的新算法[J]. 数学年刊A辑(中文版), 2014, 35(2): 247-256 |
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| 作者姓名： | 杨云青 陈勇 |
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| 作者单位： | 浙江海洋学院数理与信息学院, 浙江~ 舟山 316004.;东师范大学上海市高可信重点实验室, 上海 200062. |
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| 基金项目： | 国家自然科学基金 (No.11075055, No.11275072), 浙江省自然科学基金 (No.LQ12A01008), 高校博士点专项科研基金(No.20120076110024)和浙江海洋学院科研启动基金 |
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| 摘 要： | 基于Bell多项式,构造了获得非线性发展方程双线性形式的一个新算法,并且开发了相应的程序包.非线性发展方程与其双线性形式之间的变换可由该程序包自动推导,同时给出了一些具有代表性的实例验证了该程序包的有效性与可靠性.
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| 关 键 词： | Bell多项式 Hirota双线性形式 符号计算 |
A New Algorithm Based on Bell Polynomials to Construct Hirota Bilinear Forms ofNonlinear Evolution Equations |
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| YANG Yunqing and CHEN Yong. A New Algorithm Based on Bell Polynomials to Construct Hirota Bilinear Forms ofNonlinear Evolution Equations[J]. Chinese Annals of Mathematics, 2014, 35(2): 247-256 |
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| Authors: | YANG Yunqing and CHEN Yong |
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| Affiliation: | School of Mathematics, Physics and Information Science,Zhejiang Ocean University, Zhoushan 316004, Zhejiang, China.;Corresponding author. Shanghai Key Laboratory of Trustworthy Computing, East ChinaNormal University, Shanghai 200062, China. |
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| Abstract: | Based on Bell polynomials, a new algorithm is developed to derive theHirota bilinear forms of nonlinear evolution equations, and the correspondingMaple package is constructed. The transformation from a equation to itsbilinear form can be deducted automatically by the Maple package. Some examples are given to verify the validity of the algorithm. |
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| Keywords: | Bell polynomial Hirota bilinear form Symbolic computation |
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