Wellposedness and analytic smoothing effect for the Benjamin-Ono equation (Q1848509)

The nonlinear dispersive equation of the Benjamin-Ono type \[ \partial_t u+H_x\partial^2_\alpha u+\partial_\alpha u^2=0,\quad u(0,x)=\phi(x),\;t\in(-T,T),\;x\in\mathbb{R}, \] is studied. Here \(H_x\) denotes the Hilbert transform. The authors investigate a sufficient condition of initial data \(\phi\) on which the solution has regularizing property up to analycity.