| Abstract: | The Ostrovsky equation governs the propagation of long nonlinear surface waves in the presence of rotation. It is related
to the Korteweg-de Vries (KdV) and the Kadomtsev-Petviashvili models. KdV can be obtained from the equation in question when
the rotation parameter γ equals zero. A fundamental solution of the Cauchy problem for the linear Ostrovsky equation is presented
in the form of an oscillatory Fourier integral. Another integral representation involving Airy and Bessel functions is derived
for it. It is shown that its asymptotic expansion as γ → 0 contains the KdV fundamental solution as the zero term. The Airy
transform is used to establish some of its properties. Higher-order asymptotics for γ → 0 on a bounded time interval are obtained
for both the fundamental solution and the solution of the linear Cauchy problem for the Ostrovsky equation. |
