J Hietarinta et al 1994 J. Phys. A: Math. Gen. 27 3149 doi:10.1088/0305-4470/27/9/027
Continuous vacua in bilinear soliton equations
J Hietarinta, A Ramani and B Grammaticos
Show affiliationsWe 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(Dx)G.F=0, B(Dx)(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.
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Issue 9 (7 May 1994)
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Continuous vacua in bilinear soliton equations
J Hietarinta et al 1994 J. Phys. A: Math. Gen. 27 3149
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