  We analytically study nonlinear quasi-monochromatic plasma waves in a
two-dimensional electron system set between the two metal electrodes (gates).
We derive a nonlinear Schrodinger equation for a slow-varying envelope to
describe the waves. We find it to be of either focusing or defocusing type
depending on the parameter qd, where q is the carrier wave vector and d is the
distance between the 2DES and the gates. When qd<1.61, we have the
defocusing-type equation with the solutions in the form of dark plasma solitons
appearing against the background of the stable plane waves. Conversely, for
qd>1.61, the focusing-type equation has the solutions in the form of bright
solitons, and the plane waves are unstable. We also address the appearance of
the simplest type of breathers in the latter case. A detailed description of
the resultant nonlinear waves is given based on the parameters of the
two-dimensional electron system.
