Related papers: On the Riemann problem for the Adlam-Allen model
A general equation describing the resonant nonlinear mode-coupling among kinetic Alfv\'en waves (KAWs) is derived using nonlinear gyrokinetic theory, which can be applied to study the potentially strong spectral energy transfer of KAWs. As…
This paper presents a global air and sea temperature anomalies analysis based upon a combination of the wavelet multiresolution analysis and the scaling analysis methods of a time series. The wavelet multiresolution analysis decomposes the…
We consider linear and nonlinear waves in a stratified hydrostatic fluid within a channel of variable area, under the restriction of one-dimensional flow. We derive a modified version of Riemann's invariant that is related to the wave…
The Korteweg de Vries (KdV) equation with small dispersion is a model for the formation and propagation of dispersive shock waves in one dimension. Dispersive shock waves in KdV are characterized by the appearance of zones of rapid…
The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model…
A theoretical investigation has been made to study the cylindrical and spherical electron-acoustic shock waves (EASWs) in an unmagnetized, collisionless degenerate quantum plasma system containing two distinct groups of electrons (one…
The dispersion and damping of ion-acoustic waves in the plasma with a regularized kappa-distribution are studied. The generalized dispersion relation and damping rate are derived, which both depend significantly on the parameters alpha and…
We study the phenomena of radiative-driven shock waves using a semi-analytic model based on self similar solutions of the radiative hydrodynamic problem. The relation between the hohlraum drive temperature $T_{\mathrm{Rad}}$ and the…
The Gibbs ensemble of the truncated KdV (TKdV) equation has been shown to accurately describe the anomalous wave statistics observed in laboratory experiments, in particular the emergence of extreme events. Here, we introduce a novel…
A full analysis of all regimes for optical dispersive shock wave (DSW) propagation in nematic liquid crystals is undertaken. These dispersive shock waves are generated from step initial conditions for the optical field and are resonant in…
The nonlinear theory of two-dimensional ion-acoustic (IA) solitary waves and shocks (SWS) is revisited in a dissipative quantum plasma. The effects of dispersion, caused by the charge separation of electrons and ions and the quantum force…
Long time dynamics of the smoothed step initial value problem or dispersive Riemann problem for the Benjamin-Bona-Mahony (BBM) equation $u_t + uu_x = u_{xxt}$ are studied using asymptotic methods and numerical simulations. The catalog of…
Discrete materials composed of masses connected by strongly nonlinear links with anomalous behavior (reduction of elastic modulus with strain) have very interesting wave dynamics. Such links may be composed of materials exhibiting…
We introduce new adaptive artificial anti-diffusion (AAAD) methods for one- and two-dimensional hyperbolic systems of conservation laws. The key idea is to reduce the amount of numerical dissipation present in a given numerical method by…
Complete asymptotic expansions are developed for slow, Alfv\'en and fast magnetohydrodynamic waves at the base of an isothermal three-dimensional (3D) plane stratified atmosphere. Together with existing convergent Frobenius series solutions…
To investigate inelastic electron scattering, which is ubiquitous in various fields of study, we carry out ab initio study of the real-time dynamics of a one-dimensional electron wave packet scattered by a hydrogen atom using different…
We develop the theory of dispersive shock waves in optical fibers for the case of long-distance propagation of optical pulses, when the small Raman effect stabilizes the profile of the shock. The Whitham modulation equations are derived as…
Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…
Properties of modified plasma waves in non-linear electrodynamics are investigated. We consider a cold, uniform, collisionless, and magnetized plasma model. Initially, we also assume small amplitude waves and the non-relativistic…
The numerical simulation of nonlinear dispersive waves is a central research topic of many investigations in the nonlinear wave community. Simple and robust solvers are needed for numerical studies of water waves as well. The main…