Nonlinear Schrödinger equation for a two-dimensional plasma: Solitons, breathers, and plane wave stability
A. A. Zabolotnykh
Abstract
We analytically study nonlinear quasimonochromatic plasma waves in a two-dimensional (2D) electron system (ES) set between the two metal electrodes (gates). We derive a nonlinear Schr\"odinger 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.