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We review asymptotic stability of solitary waves for nonlinear dispersive equations set on the line. Our focus is threefold: first, the nonlinear Schrodinger equation; second, the notion of full asymptotic stability (which states that…
Recent observations of non-local transport in ultraclean 2D materials raised the tantalizing possibility of accessing hydrodynamic correlated transport of many-electron state. However, it has been pointed out that non-local transport can…
The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging…
A general equation for drift waves is derived incorporating both nonlinear electron density perturbation and ion vorticity effects. It is emphasized that the well-known Hasegawa-Mima (HM) equation for drift waves [A. Hasegawa and K. Mima,…
In this work, we study the nonlinear traveling waves in density stratified fluids with depth varying shear currents. Beginning the formulation of the water-wave problem due to [1], we extend the work of [4] and [18] to examine the interface…
We show that equations of Newtonian hydrodynamics and gravity describing one-dimensional steady gas flow possess nonlinear periodic solutions. In the case of a zero-pressure gas the solution exhibits hydrodynamic similarity and is…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
Sub-wavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene…
The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the…
The nonlinear propagation of internal gravity waves in the weakly ionized, incompressible Earth's ionosphere is studied using the fluid theory approach. Previous theory in the literature is advanced by the effects of the terrestrial…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
We consider the linear and nonlinear response of a weighted graphene sheet under the normal incidence of a plane electromagnetic wave in the form of a quasi-monochromatic pulse of long duration with a sharp edge and harmonic filling. The…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
Owing to its peculiar energy dispersion, the quantum capacitance property of graphene can be exploited in a two-dimensional layered capacitor configuration. Using graphene and boron nitride respectively as the electrodes and the insulating…
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena…
We investigate the features arising from hydrodynamic effects in graphene and phosphorene devices with finite heat sources, using ab initio calculations to go beyond Callaway's model and inform a full linearized scattering operator, and…
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength…
Nonlinear behavior of electro-osmosis in dilute non-adsorbing polymer solutions with low salinity is investigated with Brownian dynamics simulations and a kinetic theory. In the Brownian simulations, the hydrodynamic interaction between the…
In two-dimensional electron systems, plasmons are gapless and long-lived collective excitations of propagating charge density oscillations. We study the fluctuation mechanism of plasmon-assisted transport in the regime of electron…
The purpose of this review is to revisit recent results in the literature where quantum plasmas with arbitrary degeneracy degree are considered. This is different from a frequent approach, where completely degeneracy is assumed in dense…