| 深水表面波可积发展方程的行波解与分支 |
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| 引用本文： | 莫达隆,卢亮,郭秀凤.深水表面波可积发展方程的行波解与分支[J].数学杂志,2016,36(5):963-974. |
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| 作者姓名： | 莫达隆 卢亮 郭秀凤 |
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| 作者单位： | 贺州学院理学院, 广西 贺州 542899,贺州学院理学院, 广西 贺州 542899;广西混杂计算与集成电路设计分析重点实验室, 广西 南宁 530006,贺州学院理学院, 广西 贺州 542899 |
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| 基金项目： | Supported by National Natural Science Foundation of China Grants (11461021);National Natural Science Foundation of Guangxi Grant (2014GXNSFAA118028);Scientific Research Foundation of Guangxi Education Department (KY2015YB306);the open fund of Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis (HCIC201305);Scientific Research Project of Hezhou University (2012PYZK02;2015ZZZK16);Guangxi Colleges and Universities Key Laboratory of Symbolic Computation and Engineering Data Processing. |
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| 摘 要： | 本文研究了small-aspect-ratio波方程和深水表面波可积发展方程的行波解问题.利用微分方程定性理论的方法,分析了行波系统的相图分支,获得了孤立波解的精确表达式.
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| 关 键 词： | 行波解 相图分支 可积系统 表面波方程 |
| 收稿时间： | 2014/9/4 0:00:00 |
| 修稿时间： | 2015/4/7 0:00:00 |
BIFURCATIONS OF TRAVELING WAVE SOLUTIONS OF INTEGRABLE EVOLUTION EQUATIONS FOR SURFACE WAVES IN DEEP WATER |
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| MO Da-long,LU Liang and GUO Xiu-feng.BIFURCATIONS OF TRAVELING WAVE SOLUTIONS OF INTEGRABLE EVOLUTION EQUATIONS FOR SURFACE WAVES IN DEEP WATER[J].Journal of Mathematics,2016,36(5):963-974. |
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| Authors: | MO Da-long LU Liang and GUO Xiu-feng |
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| Institution: | School of Sciences, Hezhou University, Hezhou 542899, China,School of Sciences, Hezhou University, Hezhou 542899, China;Guangxi Key Laboratories of Hybrid Computation and Integrated Circuit Design Analysis, Nanning 530006, China and School of Sciences, Hezhou University, Hezhou 542899, China |
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| Abstract: | In this paper, we investigate the traveling wave solutions of a small-aspect-ratio wave equation and an integrable evolution equation for surface waves in deep water. By applying the qualitative theory of differential equations, we analyze the phase portraits of the traveling wave systems and obtain the exact explicit representations of solitary wave solutions. |
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| Keywords: | traveling wave solutions bifurcations of phase portraits integrable systems surface waves equations |
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