| PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES |
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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 |
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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.
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Received: 30 August 2023
Revised: 29 October 2023
Accepted manuscript online: 31 October 2023
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PACS:
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52.27.Lw
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(Dusty or complex plasmas; plasma crystals)
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52.65.Rr
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(Particle-in-cell method)
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52.35.Mw
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(Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))
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| Fund: 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). |
Corresponding Authors:
Heng Zhang, Wen-Shan Duan
E-mail: zhangheng@nwnu.edu.cn;duanws@nwnu.edu.cn
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Cite this article:
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 2024 Chin. Phys. B 33 025203
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