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We analytically study plasma solitary waves, or solitons, in atwo-dimensional (2D) electron system (ES) placed in close proximity to andbetween two ideal metallic gates. As a rule, solitons are described using aperturbative approach applicable only in the weak non-linearity regime. Incontrast, we analyze solitons considering a non-perturbative model. Thisframework enables an exact analytical description of the soliton shape.Moreover, it can be achieved in the regime beyond weak non-linearity -- whenthe concentration deviation due to the soliton is of the order of theequilibrium concentration. We determine the conditions required for a solitonto exist and derive the relationship between its amplitude, width, andvelocity. We believe that our results obtained for the given model can providevaluable insight into the physics of non-linear waves.

Plasma solitons in gated two-dimensional electron systems: exactly solvable analytical model for the regime beyond weak non-linearity