We present a generalized (2+1)-dimensional Boussinesq equation, including two cases which are called the plus Boussinesq equation and the minus one. To investigate these equations, we apply the $\bar{ \partial}$ approach to a coupled (2+1)-dimensional nonlinear equation, which reduces to the Boussinesq equation. For the plus equation, we give the line-solitons and rational solutions, for the minus one, we give some freak solutions.
Categories: nlin.SI