2D splash mode

Abstract

A simple solution of the wave equation with two spatial variables having a similarity to the well known splash mode solutions is presented. It depends on two free parameters and describes a localized few-cycle pulse having finite energy. The behavior of the solution is studied both in the vicinity of the focus and at large times and distances. It was found that its real part at all points and at all instants of time is strictly positive. Integral representations for the solutions are derived and an expression for its total energy is found.