Soliton solutions for the electron flow in graphene.

Abstract

In the past decades, graphene is a material of great interest. Due to its purity, electrons can move through the lattice with very low resistance. Therefore the well known Navier Stokes equations can be applied to model the electron flow. In the perturbative regime, this gives rise to nonlinear partial differential equations. The inverse scattering transform is studied to solve these equations for their soliton solutions. Furthermore the Hamiltonian structures of these equations will be analyzed and suitable methods will be used to solve them numerically.