A search for bilinear equations passing Hirota’s three-soliton condition. II. mKdV-type bilinear equations

In this paper (second in a series) [for part I, see J. Math. Phys. 30, 1732 (1987)] the search for bilinear equations having three-soliton solutions continues. This time pairs of bilinear equations of the type P1(Dx,Dt)F⋅G=0, P2(Dx,Dt)F⋅G=0, where P1 is an odd polynomial and P2 is quadratic, are considered. The main results are the following new bilinear systems: P1=aDx7+bDx5 +Dx2Dt+Dy, P2=Dx2; P1=aDx3+bDt3 +Dy, P2=DxDt; and P1=DxDtDy +aDx+bDt, P2=DxDt. In addition to these, several models with linear dispersion manifolds were obtained, as before.