  We found a new kind of soliton solutions for the 5-parameter family of the
potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the
Schr\"odinger equation. In contradistinction to the "usual'' solitons like
{\cosh[b(x-kt)]}^{-a}\exp[i(kx-ft)], the new {\em Finite-Length Solitons} (FLS)
are nonanalytical functions with continuous first derivatives, which are
different from zero only inside some finite regions of space. The simplest
one-dimensional example is the function which is equal to
{\cos[g(x-kt)]}^{1+d}\exp[i(kx-ft)] (with d>0) for |x-kt|<\pi/(2g), being
identically equal to zero for |x-kt|>\pi/(2g). The FLS exist even in the case
of a weak nonlinearity, whereas the ``usual'' solitons exist provided the
nonlinearity parameters surpass some critical values.
