| Numerical simulation of the soliton solutions for a complex modified Korteweg—de Vries equation by a finite difference method |
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| 作者姓名： | Tao Xu Guowei Zhang Liqun Wang Xiangmin xu Min Li |
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| 作者单位： | State Key Laboratory of Heavy Oil Processing;College of Science;Department of Mathematics and Physics |
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| 基金项目： | This work was parially supported by the Natural Science Foundation of Beijing Munisipality(Grant No.1212007);by the Science Foundations of China University of Petroleum,Beijing(Grant Nos.2462020YXZZ004 and 2462020XKJS02). |
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| 摘 要： | In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance.
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| 关 键 词： | complex modified Korteweg-de Vries equation finite difference method soliton solutions |
| 收稿时间： | 2020-08-22 |
Numerical simulation of the soliton solutions for a complex modified Korteweg-de Vries equation by a finite difference method |
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| Tao Xu,Guowei Zhang,Liqun Wang,Xiangmin xu,Min Li.Numerical simulation of the soliton solutions for a complex modified Korteweg-de Vries equation by a finite difference method[J].Communications in Theoretical Physics,2021,73(2):25005-51. |
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| Authors: | Tao Xu Guowei Zhang Liqun Wang Xiangmin Xu Min Li |
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| Institution: | 1.State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China;2.College of Science, China University of Petroleum, Beijing 102249, China;3.Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China |
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| Abstract: | In this paper, a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modified Korteweg-de Vries (MKdV) equation (which is equivalent to the Sasa-Satsuma equation) with the vanishing boundary condition. It is proved that such a numerical scheme has the second-order accuracy both in space and time, and conserves the mass in the discrete level. Meanwhile, the resulting scheme is shown to be unconditionally stable via the von Nuemann analysis. In addition, an iterative method and the Thomas algorithm are used together to enhance the computational efficiency. In numerical experiments, this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation. The numerical accuracy, mass conservation and linear stability are tested to assess the scheme’s performance. |
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| Keywords: | complex modified Korteweg-de Vries equation finite difference method soliton solutions |
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