Long-wave propagation in water with bottom discontinuity (Q1187552)

We have derived a KdV-type equation for the propagation of long waves, when there is a sudden change in depth due to a step-like discontinuity at the bottom. Nonlinearity and dispersion are measured by the same parameters as in the classical KdV equation. The additional effect of change in depth is taken into account by a parameter \(\varepsilon\), which is a measure of change in depth, by retaining terms inear in this parameter. We find that as \(\varepsilon\to 0\), the equation reduces to the classical KdV equation.