| Dullin-Gottwald-Holm方程的1-孤子解 |
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| 引用本文： | 居琳,田立新. Dullin-Gottwald-Holm方程的1-孤子解[J]. 江苏科技大学学报(社会科学版), 2006, 20(4): 33-37 |
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| 作者姓名： | 居琳 田立新 |
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| 作者单位： | 江苏科技大学,数理学院,江苏,镇江,212003;江苏大学,非线性科学研究中心,江苏,镇江,212013;江苏大学,非线性科学研究中心,江苏,镇江,212013 |
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| 基金项目： | 国家自然科学基金 , 江苏省自然科学基金 |
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| 摘 要： | 研究了一类由Dullin,Gottwald和Holm提出的新的含线性和非线性色散项的完全可积型浅水波方程(称为Dullin-Gottwald-Holm方程)的反散射问题。首先利用反散射方法建立了DGH方程的反散射方程以及一系列求解方程,并且给出了解的一般形式,然后利用散射数据以参数形式给出了DGH方程的1-孤子解,最后画出了几个取特殊值时解的侧面图。
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| 关 键 词： | DGH方程 1-孤子解 散射数据 反散射方法 |
| 文章编号： | 1673-4807（2006）04-0033-05 |
| 收稿时间： | 2005-11-25 |
| 修稿时间： | 2005-11-25 |
One-soliton Solution of Dullin-Gottwald-Holm Equation |
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| JU Lin,TIAN Lixin. One-soliton Solution of Dullin-Gottwald-Holm Equation[J]. Journal of Jiangsu University of Science and Technology(Natural Science Edition), 2006, 20(4): 33-37 |
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| Authors: | JU Lin TIAN Lixin |
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| Affiliation: | 1. School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang Jiangsu 212003, China;2. Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang Jiangsu 212013, China |
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| Abstract: | The inverse scattering problem for the new completely-integrable shallow water wave equation namely Dullin-Gottwald-Holm Equation is studied,in which the linear and nonlinear dispersions are included.The inverse scattering transform method is used to establish the inverse scattering equation of the DGH equation as well as a series of solving equations.The known one-soliton solution in a simple parametric form is obtained by using the scattering data.Some examples of the one-soliton solution are given in the form of profile. |
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| Keywords: | DGH equation one-soliton solution scattering data inverse scattering method |
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