Applied Scientific Research

, Volume 37, Issue 1–2, pp 21–30 | Cite as

Convergence of periodic wavetrains in the limit of large wavelength

  • Jerry L. Bona
Article

Abstract

The Korteweg-de Vries equation was originally derived as a model for unidirectional propagation of water waves. This equation possesses a special class of traveling-wave solutions corresponding to surface solitary waves. It also has permanent-wave solutions which are periodic in space, the so-called cnoidal waves. A classical observation of Korteweg and de Vries was that the solitary wave is obtained as a certain limit of cnoidal wavetrains.

This result is extended here, in the context of the Korteweg-de Vries equation. It is demonstrated that a general class of solutions of the Korteweg-de Vries equation is obtained as limiting forms of periodic solutions, as the period becomes large.

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Copyright information

© Martinus Nijhoff Publishers 1981

Authors and Affiliations

  • Jerry L. Bona
    • 1
  1. 1.Dept. of MathematicsThe University of ChicagoChicagoUSA

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