Related papers: Morphological Evolution of Higher Order Nonlinear …
The authors of the paper "Two-dimensional third- and fifth-order nonlinear evolution equations for shallow water waves with surface tension" \cite{Fok} claim that they derived the equation which generalizes the KdV equation to two space…
The nonlinear fluid theory developed by Schamel suggests a modified KdV equation to describe the temporal evolution of ion acoustic (IA) solitons in the presence of trapped electrons. The validity of this theory is studied here by verifying…
Observations of molecular clouds show the existence of starless, dense cores, threaded by magnetic fields. Observed line widths indicate these dense condensates to be embedded in a supersonically turbulent environment. Under these…
Perturbations commonly added to the KdV equation contain terms that represent inelastic interac-tions among KdV solitons in multiple-soliton solutions. These terms trigger the emergence of new waves in the first-order correction to the…
We study existence of helical solitons in the vector modified Korteweg-de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems,…
The nature of the plasma wave modes around the ion kinetic scales in highly Alfv\'enic slow solar wind turbulence is investigated using data from the NASA's Parker Solar Probe taken in the inner heliosphere, at 0.18 Astronomical Unit (AU)…
The dispersion and damping rate of kinetic Alfv\'en waves are studied in temperature anisotropic space plasma with kappa-Maxwellian distribution. Employing a kinetic approach, the wave frequency and damping rate of kinetic Alfv\'en waves…
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…
Magnetohydrodynamic instabilities like Toroidal Alfv\'en Eigenmodes or core-localized modes such as Beta Induced Alfv\'en Eigenmodes and Reversed Shear Alfv\'en Eigenmodes driven by fast particles can lead to significant redistribution and…
The Kelvin-Helmholtz instability (KHI) can occur when there is a relative motion between two adjacent fluids. In the case of magnetized plasma, the shear velocity must exceed the local Alfv\'{e}n speed for the instability to develop. The…
Particles ejected from the Sun that stream through the surrounding plasma of the solar wind are causing instabilities. These generate wavemodes in a certain frequency range especially within shock regions, where particles are accelerated.…
The internal-wave (IW) continuum of a regional ocean model is studied in terms of the vertical spectral kinetic-energy (KE) fluxes and transfers at high vertical wavenumbers. Previous work has shown that this model permits a partial…
It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly…
Understanding the nature of charge density wave (CDW) and superconductivity in kagome metal AV$_3$Sb$_5$ (A=Cs,Rb,K) is a recent subject of intensive study. Due to the presence of van Hove singularities, electron-electron interaction has…
Under the effect of common perturbations, the multiple-soliton solution of the KdV equation is transformed into a sum of an elastic and a first-order inelastic component. The elastic component is a perturbation series, identical in…
Magnetohydrodynamic kink waves naturally form as a consequence of perturbations to a structured medium, for example transverse oscillations of coronal loops. Linear theory has provided many insights in the evolution of linear oscillations,…
We demonstrate that in highly magnetized pair plasmas, nonlinear Alfven waves with wave-number $k \leq k_0 = \omega_p^2 /(\delta \omega_B)$ ($\delta =( \delta B)/B_0$ are relative fluctuations of the magnetic field) experience powerful…
We investigate the soliton structure of novel (2+1)-dimensional nonlinear partial differential evolution(NLPDE) equations which may govern the behavior of a barothropic relaxing medium beneath high-frequency perturbations. As a result, we…
We investigate compressive turbulence at sub-ion scales with measurements from the Magnetospheric MultiScale Mission. The tetrahedral configuration and high time resolution density data obtained by calibrating spacecraft potential allow an…
Recent numerical studies revealed that transverse motions of coronal loops can induce the Kelvin-Helmholtz Instability (KHI). This process could be important in coronal heating because it leads to dissipation of energy at small…