Propagation of long waves of finite amplitude

Abstract

We consider the radiation problem for long waves of- small amplitude, caused by an instantaneous disturbance of unit height at the origin. The equations governing this phenomrnon were derived by Long (1964). The asymptotic expressions for the wave front and for large times are obtained. The initial value problem for the non-linear system of equations is also solved, using a perturbation scheme based on the small parameter α, the non-dimensional amplitude of the disturbance. The sofution holds only for t < < I / α as a result of the appearance of a secular term in the fist order solution.