Effects of Dissipation on Solitons in the Hydrodynamic Regime of Graphene

We use hydrodynamic techniques to analyze the one-dimensional propagation of solitons in gated graphene on an arbitrary uniform background current. Results are derived for both the Fermi liquid and Dirac fluid regimes. We find that these solutions satisfy the Korteweg-de Vries-Burgers equation. Viscous dissipation and ohmic heating are included, causing the solitons to decay. Experiments are proposed to measure this decay and thereby quantify the shear viscosity in graphene.