| 一类非线性方程的函数级数解法 |
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| 引用本文： | 兰慧彬 汪克林. 一类非线性方程的函数级数解法[J]. 中国科学技术大学学报, 1990, 20(1): 15-26 |
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| 作者姓名： | 兰慧彬 汪克林 |
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| 作者单位： | 中国科学技术大学基础物理中心(兰慧彬)，中国科学技术大学基础物理中心(汪克林) |
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| 摘 要： | 本文首次用双曲正割和双曲正切的函数幂级数表示一类非线性方程的特定解,在参数受到某些限制时,这种函数级数解可以被截断为只有几项的形式——截断解.我们既给出了高重(七重)KdV 方程和一些其他具非线性背景势作用的非线性方程的函数级数解,又给出了相应的截断解.
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| 关 键 词： | 非线性方程 函数级函数解 数学物理 |
The Method of Function Series for Solving a Kind of Nonlinear Equations |
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| Lan Huibin Wang Kelin Centre for Fundamental Physics. The Method of Function Series for Solving a Kind of Nonlinear Equations[J]. Journal of University of Science and Technology of China, 1990, 20(1): 15-26 |
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| Authors: | Lan Huibin Wang Kelin Centre for Fundamental Physics |
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| Affiliation: | Lan Huibin Wang Kelin Centre for Fundamental Physics |
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| Abstract: | This paper states that,for the first time,the power series of hyperbolictangent and hyperbolic secant has been used to represent a specified solutionfor a kind of nonlinear equation.Under some constraints of the parameters,this function series solution can be terminated into a form containing only afew terms terminating solution.The paper provides not only the function ser-ies solutions for the highth(7th)KdV equation and some other nonlinear equa-tions with nonlinear substrate potential interaction,but also the realated ter-minating solutions. |
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| Keywords: | solution of function series terminating solution mathematical Physics |
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