Kac–Moody–Virasoro symmetry algebra and symmetry reductions of the bilinear sinh-Gordon equation in (2 + 1)-dimensions

Abstract

By means of the formal series symmetry approach proposed in [1], infinite many symmetries and the corresponding Kac–Moody–Virasoro Lie symmetry algebra of a new bilinear (2 + 1)-dimensional sinh-Gordon equation are given. Then, the obtained symmetries are used to get the symmetry reductions of the model. From one of the special reduction we know that the bilinear form of the first member of the negative Kadomtsev–Petviashvili hierarchy is not only a (2 + 1)-dimensional sinh-Gordon extension but also a novel (2 + 1)-dimensional classical Boussinesq extension.