Applied Scientific Research

, Volume 37, Issue 1, pp 21–30

Convergence of periodic wavetrains in the limit of large wavelength

  • Jerry L. Bona

DOI: 10.1007/BF00382614

Cite this article as:
Bona, J.L. Applied Scientific Research (1981) 37: 21. doi:10.1007/BF00382614


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.

Copyright information

© Martinus Nijhoff Publishers 1981

Authors and Affiliations

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