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International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 4, Pages 811-817
http://dx.doi.org/10.1155/S0161171283000691

Modulational stability of Korteweg-de Vries and Boussinesq wavetrains

1Physical Research Laboratory, Ahmedabad 380 009, India
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA
3Institute of Mathematical Sciences, Madras 600 113, India

Copyright © 1983 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The modulational stability of both the Korteweg-de Vries (KdV) and the Boussinesq wavetrains is investigated using Whitham's variational method. It is shown that both KdV and Boussinesq wavetrains are modulationally stable. This result seems to confirm why it is possible to transform the KdV equation into a nonlinear Schrödinger equation with a repulsive potential. A brief discussion of Whitham's variational method is included to make the paper self-contained to some extent.