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

Nonlinear Schrodinger equation for a two-dimensional plasma: the analysis of solitons, breathers, and plane wave stability