Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes

doi:10.1088/1674-1056/ad082b

中国物理B ›› 2024, Vol. 33 ›› Issue (2): 25203-025203.doi: 10.1088/1674-1056/ad082b

Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes

Yu-Xi Chen(陈羽西), Heng Zhang(张恒)^†, and Wen-Shan Duan(段文山)^‡

College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

收稿日期:2023-08-30 修回日期:2023-10-29 接受日期:2023-10-31 出版日期:2024-01-16 发布日期:2024-01-19
通讯作者: Heng Zhang, Wen-Shan Duan E-mail:zhangheng@nwnu.edu.cn;duanws@nwnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11965019 and 42004131) and the Foundation of Gansu Educational Committee (Grant No. 2022QB-178).

Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes

Yu-Xi Chen(陈羽西), Heng Zhang(张恒)^†, and Wen-Shan Duan(段文山)^‡

College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

Received:2023-08-30 Revised:2023-10-29 Accepted:2023-10-31 Online:2024-01-16 Published:2024-01-19
Contact: Heng Zhang, Wen-Shan Duan E-mail:zhangheng@nwnu.edu.cn;duanws@nwnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11965019 and 42004131) and the Foundation of Gansu Educational Committee (Grant No. 2022QB-178).

摘要/Abstract

摘要： The present paper chooses a dusty plasma as an example to numerically and analytically study the differences between two different methods of obtaining nonlinear Schrödinger equation (NLSE). The first method is to derive a Korteweg-de Vries (KdV)-type equation and then derive the NLSE from the KdV-type equation, while the second one is to directly derive the NLSE from the original equation. It is found that the envelope waves from the two methods have different dispersion relations, different group velocities. The results indicate that two envelope wave solutions from two different methods are completely different. The results also show that the application scope of the envelope wave obtained from the second method is wider than that of the first one, though both methods are valuable in the range of their corresponding application scopes. It is suggested that, for other systems, both methods to derive NLSE may be correct, but their nonlinear wave solutions are different and their application scopes are also different.

关键词: dusty plasmas, nonlinear waves, particle-in-cell simulation

Abstract: The present paper chooses a dusty plasma as an example to numerically and analytically study the differences between two different methods of obtaining nonlinear Schrödinger equation (NLSE). The first method is to derive a Korteweg-de Vries (KdV)-type equation and then derive the NLSE from the KdV-type equation, while the second one is to directly derive the NLSE from the original equation. It is found that the envelope waves from the two methods have different dispersion relations, different group velocities. The results indicate that two envelope wave solutions from two different methods are completely different. The results also show that the application scope of the envelope wave obtained from the second method is wider than that of the first one, though both methods are valuable in the range of their corresponding application scopes. It is suggested that, for other systems, both methods to derive NLSE may be correct, but their nonlinear wave solutions are different and their application scopes are also different.

Key words: dusty plasmas, nonlinear waves, particle-in-cell simulation

中图分类号: (Dusty or complex plasmas; plasma crystals)

52.27.Lw

52.65.Rr (Particle-in-cell method) 52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))

Yu-Xi Chen(陈羽西), Heng Zhang(张恒), and Wen-Shan Duan(段文山). Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes[J]. 中国物理B, 2024, 33(2): 25203-025203.

Yu-Xi Chen(陈羽西), Heng Zhang(张恒), and Wen-Shan Duan(段文山). Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes[J]. Chin. Phys. B, 2024, 33(2): 25203-025203.

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Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes

Differences between two methods to derive a nonlinear Schrödinger equation and their application scopes

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