Abstract. We discuss the freedom in the background field (vacuum) on top of which the solitons are built. If the Hirota bilinear form of a soliton equation is given by A(D_x)G.F=0, B(D_x)(F.F-G.G)=0, where both A and B are even polynomials in their variables, then there can be a continuum of vacua, parametrized by a vacuum angle phi . The ramifications of this freedom for the construction of one- and two-soliton solutions are discussed. We find, for example, that once the angle phi is fixed and we choose u=tan^-1 G/F as the physical quantity, then there are four different solitons (or kinks) connecting the vacuum angles +or- phi , +or- phi +or- pi /2 (where pi is the defined modulo). The most interesting result is the existence of a 'ghost' soliton; goes over to the vacuum but interacts with 'normal' solitons by giving them a finite phase shift.

Print publication: Issue 9 (7 May 1994)