  We elaborate a model of the interferometer which, unlike previously studied
ones, uses a local (delta-functional) nonlinear repulsive potential, embedded
into a harmonic-oscillator trapping potential, as the splitter for the incident
soliton. An estimate demonstrates that this setting may be implemented by means
of the localized Feshbach resonance controlled by a focused laser beam. The
same system may be realized as a nonlinear waveguide in optics. Subsequent
analysis produces an exact solution for scattering of a plane wave in the
linear medium on the delta-functional nonlinear repulsive potential, and an
approximate solution for splitting of the incident soliton when the ambient
medium is nonlinear. The most essential result, obtained by means of systematic
simulations, is that the use of the nonlinear splitter provides the sensitivity
of the soliton-based interferometer to the target, inserted into one of its
arms, which is much higher than the sensitivity provided by the usual linear
splitter.
