On the generalized reduced Ostrovsky equation

Abstract

We survey recent progress on the case of the Cauchy problem for the generalized reduced Ostrovsky equation ut=S(∂x)u+(f(u))x, where the operator S(∂x) is defined through the Fourier transform as S(∂x)=ℱ−11iξℱ, and the nonlinear interaction is given by f(u)=|u|ρ−1u if ρ> 1 is not an integer and f(u)=uρ if ρ> 1 is an integer.