  Within the framework of the Inverse-Scattering formalism and the Hirota
algorithm, soliton solutions of evolution equations are images of
{\tau}-functions. Typically, the latter are expressed in terms of exponentials,
the arguments of which are linear in the coordinates. Consequently, often,
{\tau}-functions are unbounded in space and time. However, they are not unique.
Exploitation of their non-uniqueness uncovers physically interesting
possibilities: 1) One can construct equivalent {\tau}-functions, which generate
the same traditional (Inverse-Scattering/Hirota)) soliton solutions, yet allow
for the extension of the family of soliton solutions to a wider, parametric
family, in which the traditional solutions are a subset. The parameters are
shifts in individual soliton trajectories. 2) When two wave numbers in a
multi-soliton solution are made to coincide, the reduction of the solution to
one with a lower number of solitons is qualitatively different for solutions
that are within the traditional subset and those that are outside this subset.
3) One can construct {\tau}-functions that are bounded in space and time, in
terms of which soliton solutions become images of localized sources.
