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Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…

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…

Hydrodynamic electron transport arises when carrier kinetics are dominated by interelectron collisions rather than the relaxation of momentum out of the electron system. In recent years, signatures of electron hydrodynamics have been…

The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of \emph{genuine nonlinearity}, namely the ability for shocks and rarefactions to form instead of…

We introduce the idea that the electronic band structure of a charge density wave system may mimic the electronic structure of graphene. In that case a class of materials quite different from graphene might be opened up to exploit…

Electrons behave like a classical fluid with a momentum distribution function that varies slowly in space and time when the quantum mechanical carrier-carrier scattering dominates over all other scattering processes. Recent experiments in…

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves,…

The linear energy dispersion of graphene electrons leads to a strongly nonlinear electromagnetic response of this material. We develop a general quantum theory of the third-order nonlinear local dynamic conductivity of graphene…

Hydrodynamic electron flow is experimentally observed in the differential resistance of electrostatically defined wires in the two-dimensional electron gas in (Al,Ga)As heterostructures. In these experiments current heating is used to…

Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective…

We present an effective hydrodynamic theory of electronic transport in graphene in the interaction-dominated regime. We derive the emergent hydrodynamic description from the microscopic Boltzmann kinetic equation taking into account…

We report a linear-scaling numerical method for exploring nonequilibrium electron dynamics in systems of arbitrary complexity. Based on the Chebyshev expansion of the time evolution of the single-particle density matrix, the method gives…

We present a comprehensive theory of the Dyakonov-Shur (DS) plasma instability in current-biased graphene transistors. Using the hydrodynamic approach, we derive equations describing the DS instability in the two-dimensional electron fluid…

We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation.…

Modern two dimensional conductors with low defect densities and strong electron-electron scattering are favorable platforms for formation of a viscous fluid of conduction electrons. Electric properties of these systems are determined by the…

Linear and nonlinear ion-acoustic waves are studied in a fluid model for non-relativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac…

Graphene, the first truly two-dimensional (one atom thin) material, possesses strongly nonlinear electrodynamic and optical properties. At low (microwave, terahertz) frequencies this results from the unique electronic property of graphene -…

Within the standard perturbative approach of Peierls, a charge-density wave is usually assumed to have a cosine shape of weak amplitude. In nonlinear physics, we know that waves can be deformed. What are the effects of the nonlinearities of…

We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…

Van der Waals heterostructures display a rich variety of unique electronic properties. To identify novel transport mechanisms, nonlocal measurements have been widely used, wherein a voltage is measured at contacts placed far away from the…