On the generalized reduced Ostrovsky equation

Abstract

We survey recent progress on the case of the Cauchy problem for the generalized reduced Ostrovsky equation $u_t=S({\partial }_x)u+{(f(u))}_x$, where the operator $S({\partial }_x)$ is defined through the Fourier transform as $S({\partial }_x)={ℱ}^{-1}\frac{1}{i\xi }ℱ$, and the nonlinear interaction is given by $f(u)=|u{|}^{\rho -1}u$ if is not an integer and $f(u)=u^{\rho }$ if is an integer.