Nonlinear Wave Modeling
In this paper, we study theoretically the evolution of leading waves due to a sudden disturbance. We first revisit the asymptotic solutions of linear dispersive equations for the leading wave train caused by a surface disturbance in a constant depth. The applicability of these theoretical predictions is then examined. Finally, we attempt to explore the connection between the profiles of the asymptotic solutions and the familiar sinusoidal waves and solitary waves.