  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.
