Reduction of soliton equations in bilinear form

It is shown that a variety of soliton equations including the KdV equation, the modified (or Gardner) equation, and the Boussinesq equation, the modified Boussinesq equation, the coupled KdV equation, the classical Boussinesq equation and the nonlinear Schrödinger equation exhibiting dark-soliton are obtained by “reductions” of the hierarchy of the KP (Kadomtsev-Petviashvili) equation in bilinear form. A reduction of the BKP equation generates the “KdV + Sawada-Kotera equation” which exhibits resonances of solitons.