Abstract
Unique features of nonlinear solitary plasmon excitations in two and three dimensional massless Dirac fluids, with respect to their normal Fermi counterparts, are explored using the Bernoulli pseudopotential method. It is revealed that graphene, as a two dimensional Dirac fluid, possesses some unique characteristics with respect to the propagation of the localized plasmon excitations, which is absent in other ordinary solids. It is also shown that the Mach number limit below/above, which the localized solitary/periodic excitations propagate in a monolayer graphene has a universal value independent of the other environmental parameters such as the electron number-density and the ambient temperature. The amplitude of nonlinear solitary or periodic waves is also remarked to be independent of such parameters and depend only on the Mach-number value of the solitary or periodic excitations. These unique hydrodynamic wave features of the massless Dirac fluid are attributed to the remarkable photon-like linear energy dispersion in Dirac points of graphene material.
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