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

Modulational stability of Korteweg-de Vries and Boussinesq wavetrains

Bhimsen K. Shivamoggi1,3 and Lokenath Debnath2

 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

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.