Multidimensional nonlinear evolution equations and inverse scattering (Q1083618)

The authors present a very nice up to date survey of recent progress on the ''complete solvability'' of nonlinear evolution equations by use of inverse scattering. Their analysis includes the Kadomtsev-Petviashvili equation for \(u=u(x,y,t)\), that is \[ (1)\quad (u_ t-6uu_ x+u_{xxx})_ x+3\lambda^ 2u_{yy}=0. \] To solve (1) through inverse scattering they reformulate it as a ''\({\bar \partial}\) problem''. This beautiful idea was first introduced by R. Beals and R. R. Coifman around six years ago and seems to be an efficient tool to study multidimensional inverse scattering problems. This paper is nice written and we recommend it to applied mathematicians and physicists as well.