KDV limit of the hydromagnetic waves in cold plasma

  • Xueke Pu
  • Min LiEmail author


In this paper, we study the long wavelength limit for the hydromagnetic waves propagating across a magnetic field in cold plasma. Based on the Gardner–Morikawa transform and the reductive perturbation method, it is demonstrated that as \(\varepsilon \rightarrow 0\), the solutions of such hydromagnetic waves converge to the solution of the Korteweg–de Vries equation on an \(O(\varepsilon ^{-3/2})\) time interval.


KdV limit Hydromagnetic waves in cold plasma Uniform energy estimates 

Mathematics Subject Classification

Primary 76Y05 35B40 35C20 Secondary 35Q35 



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Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceGuangzhou UniversityGuangzhouPeople’s Republic of China
  2. 2.Faculty of Applied MathematicsShanxi University of Finance and EconomicsTaiyuanPeople’s Republic of China

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