ABSTRACT
This chapter derives the system of hydrodynamic equations governing the collective motion of massless fermions in graphene. The obtained equations demonstrate the lack of Galilean and Lorentz invariance, and contain a variety of nonlinear terms due to quasirelativistic nature of carriers. The chapter shows the possibility of soliton formation in electron plasma of gated graphene. The quasirelativistic effects set an upper limit for soliton amplitude, which marks graphene out of conventional semiconductors. The most natural way to account for carrier-carrier interactions in transport models is to use local equilibrium hydrodynamic distribution functions as a first approximation to the solution of kinetic equation. The chapter presents an explicit derivation of hydrodynamic equations for massless electrons in graphene, following the general strategy put forward by Achiezer et al. Hydrodynamics proved to be an extremely efficient tool for the study of electron plasma in two-dimensional electron systems.
