Extended KdV equation for transient axisymmetric water waves

Abstract The equation for non-linear water waves in shallow water with cylindrical symmetry is established in the form of the Extended KdV (EKdV) equation. The method of solution is based on the Split Step Fourier Algorithm. It is applicable in both directions; that is, given a wave record near the origin, the theory predicts the wave evolution. Similarly, given a wave record at a distance from the origin, the method is able to predict the original wave near the origin. Theory is applied to and verified by transient wave records obtained from underwater explosions and by dropping a large cylindrical plate in very shallow water. The difference between the KdV and the Extended KdV equation is emphasized for small valuev of Ursell parameter.