| KdV-Burgers方程行波解的稳定性 |
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| 引用本文： | 石玉仁,封文星,席忠红,宗谨,宋宗斌,庞军刚.KdV-Burgers方程行波解的稳定性[J].计算物理,2018,35(2):178-186. |
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| 作者姓名： | 石玉仁 封文星 席忠红 宗谨 宋宗斌 庞军刚 |
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| 作者单位： | 1. 西北师范大学 物理与电子工程学院, 兰州 730070;2. 甘肃民族师范学院 物理与水电工程系, 合作 747000 |
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| 基金项目： | 国家自然科学基金（11565021，11047010）及西北师范大学青年教师科研能力提升计划（NWNU-LKQN-16-3）资助项目 |
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| 摘 要： | 对KdV-Burgers方程的行波解进行线性稳定性分析，数值结果表明：对于正耗散情形，其行波解是稳定的；对于负耗散情形，其行波解是不稳定的.其次构造有限差分法对其行波解进行非线性动力学演化，结果表明：对于正耗散情形，KdV-Burgers方程的行波解是稳定的.本文结果修正和完善了相关文献中所得结论.
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| 关 键 词： | KdV-Burgers方程 行波解 稳定性 |
| 收稿时间： | 2017-01-03 |
| 修稿时间： | 2017-05-03 |
Dynamical Stability of Traveling Wave Solutions to KdV-Burgers Equation |
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| SHI Yuren,FENG Wenxing,XI Zhonghong,ZONG Jin,SONG Zongbin,PANG Jungang.Dynamical Stability of Traveling Wave Solutions to KdV-Burgers Equation[J].Chinese Journal of Computational Physics,2018,35(2):178-186. |
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| Authors: | SHI Yuren FENG Wenxing XI Zhonghong ZONG Jin SONG Zongbin PANG Jungang |
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| Institution: | 1. College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China;2. College of Physics and Hydropower Engineering, Gansu Normal University For Nationalities, Hezuo 747000, China |
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| Abstract: | We made linearization stability analysis on traveling wave solutions of KdV-Burgers equation. Numerical results indicate that traveling waves are dynamically stable for positive-dissipation case, while they are dynamically unstable for negative-dissipation case. Then we presented a finite difference scheme, which is conditionally stable, for long-time evolution of perturbed traveling waves. Numerical results also show that traveling waves are dynamically stable as positive-dissipation is held. Our results modify and improve conclusions given in relative literatures. |
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| Keywords: | KdV-Burgers equation traveling wave solution dynamical stability |
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