| (2+1)维色散长波系统的局域分形结构 |
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| 引用本文： | 黄磊,孙建安,豆福全.(2+1)维色散长波系统的局域分形结构[J].西北师范大学学报,2006,42(5):43-46,80. |
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| 作者姓名： | 黄磊 孙建安 豆福全 |
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| 作者单位： | 西北师范大学物理与电子工程学院,甘肃兰州730070 |
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| 摘 要： | 利用拓展的Riccati方程映射法，进一步研究了（2＋1）维色散长波系统，得到了方程的1组新的舍有2个任意函数的分离变量解．分别选取2个任意函数为Jacobi椭圆正弦函数和Jacobi椭圆余弦函数的适当组合，借助教学软件Mathematica，得到了系统的随机分形结构和规则分形结构．结果表明，分形结构不仅出现在不可积系统中，也会出现在可积系统中。
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| 关 键 词： | Riccati方程映射法 色散长波(DLW)方程 分离变量 局域分形结构 |
| 文章编号： | 1001-988X（2006）05-0043-04 |
| 收稿时间： | 2006-03-08 |
| 修稿时间： | 2006-03-082006-06-02 |
Localized fractal structure of (2+1)-dimensional dispersive long-water wave system |
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| HUANG Lei,SUN Jian-an,DOU Fu-quan.Localized fractal structure of (2+1)-dimensional dispersive long-water wave system[J].Journal of Northwest Normal University Natural Science (Bimonthly),2006,42(5):43-46,80. |
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| Authors: | HUANG Lei SUN Jian-an DOU Fu-quan |
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| Institution: | College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, Gansu, China |
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| Abstract: | By means of an extended Riccati equation mapping approach,a new type of variable separation solutions with two arbitrary functions of(2 1)-dimensional dispersive long-water wave(DLW) system are derived.With the help of the Mathematica,new localized stochastic fractal structures and regular fractal structures of(2 1)-dimensional DLW system are obtained by selecting the two arbitrary functions as the combination of the Jacobi elliptic sine functions and the Jacobi elliptic cosine functions respectively.The results indicate that the fractal structures not only exist in the non-integrabel systems but also exist in the integrabel systems. |
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| Keywords: | Riccati equation mapping approach dispersive long-water wave(DLW) system variable separation localized fractal structures |
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