A vector \(\bar\partial\)-problem and self-similar solutions of the Kadomtsev-Petviashvili equation (Q1814549)

Using the vector \(\overline\partial\)-analogue of the Riemann-Hilbert problem, the author finds self-similar solutions of two types of Kadomtsev-Petviashvili equations: \[ (\partial/\partial x)(4u_ t+6uu_ x-u_{xxx})+3u_{yy}=0,\quad(\partial/\partial x)(4u_ t+6uu_ x- u_{xxx})-3u_{yy}=0. \] The classes of real-valued solutions are also singled out.