Nonlinearization of the KdV-type and mKdV-type bilinear equations

In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations (in the sense having 3-soliton solutions) of the KdV type and mKdV type that were found by Jarmo Hietarinta in 1980s. Examples of non-integrable bilinear equations of the KdV type are also given.