THE MKDV-ZK LIMIT OF THE EULER-POISSON SYSTEM AT CRITICAL DENSITIES

Xiaoyu Xi; Meiling Zhang

doi:10.11948/20240465

2026 Volume 16 Issue 3

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Xiaoyu Xi, Meiling Zhang. THE MKDV-ZK LIMIT OF THE EULER-POISSON SYSTEM AT CRITICAL DENSITIES[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1298-1324. doi: 10.11948/20240465

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Xiaoyu Xi, Meiling Zhang. THE MKDV-ZK LIMIT OF THE EULER-POISSON SYSTEM AT CRITICAL DENSITIES[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1298-1324. doi: 10.11948/20240465

THE MKDV-ZK LIMIT OF THE EULER-POISSON SYSTEM AT CRITICAL DENSITIES

Xiaoyu Xi^1,,
Meiling Zhang^1, ,

1.
School of Mathematics and Information Science, Guangzhou University, 510006 Guangzhou, China

Author Bio: Email: sxxixiaoyu@gzhu.edu.cn(X. Xi)
Corresponding author: Email: zml2112215061@foxmail.com(M. Zhang)

Abstract

Abstract

This paper focuses on the long wavelength limit for the Euler-Poisson system arising in plasma including three species in three dimensional case. The goal here is to deduce rigorously the modified Korteweg-de Vries-ZK (mKdV-ZK) equation, under the Gardner-Morikawa transform $ \varepsilon^{1/2}(x_1-Vt)\to x_1, \varepsilon^{1/2}x_2\to x_2, \varepsilon^{1/2}x_3\to x_3, \varepsilon^{3/2}t\to t, $ as $ \varepsilon\rightarrow0$. By employing delicate energy method, we give uniform in $ \varepsilon$ estimate for the error between the mKdV-ZK equation and the Euler-Poisson system.
- Euler-Poisson equation /
- long wavelength limit /
- modified Korteweg-de Vries-ZK (mKdV-ZK) equation
MSC: 35L30, 46B06, 47G20

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References

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