| 高维弱扰动破裂孤子波方程行波解 |
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| 引用本文： | 张良,林万涛,陈贤峰,莫嘉琪. 高维弱扰动破裂孤子波方程行波解[J]. 应用数学和力学, 2015, 36(11): 1204-1210. DOI: 10.3879/j.issn.1000-0887.2015.11.008 |
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| 作者姓名： | 张良 林万涛 陈贤峰 莫嘉琪 |
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| 作者单位： | 1亳州师范高等专科学校 电子与信息工程系, 安徽 亳州 236800;2大气科学和地球流体力学数值模拟国家重点实验室(中国科学院 大气物理研究所), 北京 100029;3上海交通大学 数学系, 上海 200240;4安徽师范大学 数学系, 安徽 芜湖 241003 |
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| 基金项目： | 国家自然科学基金(41275062;11371248);安徽省教育厅自然科学课题(KJ2015A347;KJ2013B153) |
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| 摘 要： | 研究了一类高维弱扰动破裂孤子波方程.首先讨论了对应的典型破裂孤子波方程, 利用待定系数投射方法得到了孤子波精确解.再利用泛函分析和摄动理论得到了原弱扰动破裂孤子波方程的孤子行波渐近解.最后, 举出例子说明了用该方法得到的弱扰动破裂孤子波方程的行波渐近解具有简捷、有效和较高精度的优点.
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| 关 键 词： | Korteweg-de Vries方程 弱扰动 渐近解 |
| 收稿时间： | 2015-06-15 |
Travelling Solutions to High-Dimensional Weakly Perturbed Breaking Soliton Wave Equations |
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| Abstract: | A class of high-dimensional weakly perturbed breaking solitary wave equations were studied. Firstly, the corresponding typical breaking solitary wave equations were considered. The exact solitary wave solution was obtained with the throwing method of undetermined coefficients. Then, the travelling wave asymptotic solution to the original weakly perturbed breaking solitary wave equation was found through functional analysis based on the perturbation theories. Finally, with an example, the proposed travelling wave asymptotic solution to the weakly perturbed breaking solitary wave equation shows the merits of simpleness, validity and good accuracy. |
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