Finding of $N$-soliton solutions of multidimensional nonlinear equations by means of Hirota's method

An infinite set of multidimensional nonlinear equations is proposed for which Hirota's method can be used to construct one-soliton and two-soliton solutions. Some of these equations have $N$-soliton solutions for any $N$. For each of the proposed equations, a family of rational solutions is constructed. It is shown that in the case of three independent variables, this family contains two-dimensional solitons.