Solitary waves and fundamental solution for Ostrovsky equation

Abstract

The Ostrovsky equation describes the propagation of one-dimensional long waves in shallow water in the presence of rotation (Coriolis effect). In this model dispersion is taken into account and dissipation is neglected. It is proved that existence and non-existence of solitary waves depends on the sign of the dispersion parameter which can be either positive or negative. A fundamental solution of the linear Cauchy problem for Ostrovsky equation is constructed. Special function representation for it is obtained. Some properties of the fundamental solution are established and its higher-order asymptotics is obtained as the rotation parameter tends to zero.