  The spatial distribution of the incompressible edge states (IES) is obtained
for a geometry which is topologically equivalent to an electronic Mach-Zehnder
interferometer, taking into account the electron-electron interactions within a
Hartree type self-consistent model. The magnetic field dependence of these IES
is investigated and it is found that an interference pattern may be observed if
two IES merge or come very close, near the quantum point contacts. Our
calculations demonstrate that, being in a quantized Hall plateau does not
guarantee observing the interference behavior.
