A new solution approach to the Serre equations

Abstract This paper concerns constructing a semi-analytic solution procedure for integrating the fully non-linear Serre equations (or 1D Green–Naghdi equations for constant water depth). The validity of the solution procedure is checked by investigating a moving solitary wave for which the analytical solution is known. The semi-analytic procedure constructed in this study is confirmed to be good at observing non-linear wave phenomena of the collision of a sufficiently high-amplitude solitary wave with a vertical wall. The simulated results are in a good agreement with data of other authors. Further, the procedure simulates the non-linear interaction of four solitary waves, which enables us to investigate the repeated reflection of a single solitary wave between two vertical walls.