FINITE-LENGTH SOLITON-SOLUTIONS OF THE LOCAL HOMOGENEOUS NONLINEAR SCHRODINGER-EQUATION

We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifica tions of the Schrodinger equation. In contradistinction to the ''usual '' solitons Like {cosh [beta(x - kt)]}(-alpha) exp [i(kx - omega t)], the new Finite-Length Solitons (FLS) are nonanalytical functions with continuous first derivatives, which are different from zero only insid e some finite regions of space. The simplest one-dimensional example i s the function which is equal to {cos [gamma(x - kt)]}(1+delta) exp [i (kx - omega t)] (with delta > 0) for \x - kt\ < pi/2 gamma, being iden tically equal to zero for \x - kt\ greater than or equal to pi/2 gamma . The FLS exist even in the case of a weak nonlinearity,whereas the '' usual'' solitons exist provided the nonlinearity parameters surpass so me critical values.