Modulational stability of Korteweg-de Vries and Boussinesq wavetrains - Bhimsen K. Shivamoggi; Lokenath Debnath (International Journal of Mathematics and Mathematical Sciences)
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.