Related papers: Analytical solutions for nonlinear plasma waves wi…
In this paper we discuss some exact results related to the fractional Klein--Gordon equation involving fractional powers of the D'Alembert operator. By means of a space-time transformation, we reduce the fractional Klein--Gordon equation to…
We determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel-Korteweg-de Vries-Zakharov-Kuznetsov (SKdVZK) equation which governs…
This paper provides a new analytical method to obtain Green's functions of linear dispersive partial differential equations. The Euler-Bernoulli beam equation and the one-dimensional heat conduction equation (dissipation equation) under…
We incorporate a time-independent gravitational field into the BGK scheme for numerical hydrodynamics. In the BGK scheme the gas evolves via an approximation to the collisional Boltzmann equation, namely the Bhatnagar-Gross-Krook (BGK)…
The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit…
We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates of weakly interacting alkali atoms described by a nonlinear Gross-Pitaevskii (GP) equation. We suggest a pseudospectral method involving Laguerre…
We study bidirectional one-dimensional (1-D) shallow-water waves within a class of Boussinesq equations, including the integrable Kaup-Boussinesq (KB) equation and a truncated-dispersion variant, which serves as a representative…
We evaluate the computational performance of the Bernstein-Bezier basis for discontinuous Galerkin (DG) discretizations and show how to exploit properties of derivative and lift operators specific to Bernstein polynomials for an optimal…
The orbital evolution of binary black hole (BBH) systems is determined by the component masses and spins of the black holes and the governing gravity theory. Gravitational wave (GW) signals from the evolution of BBH orbits offer an…
The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov--Poisson--Lenard--Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
We study the linearized Vlasov equations and the linearized Vlasov-Fokker-Planck equations in the weakly collisional limit in a uniform magnetic field. In both cases, we consider periodic confinement and Maxwellian (or close to Maxwellian)…
The solution to the non-forward BFKL equation in the Leading Logarithmic approximation is expressed in terms of a sum of iterations of its kernel directly in transverse momentum and rapidity space. Several studies of the non-forward…
In this article, we study the generalised Kudryashov method for the time fractional generalized Burgers-Fisher equation (GBF). Using traveling wave transformation, the time fractional GBF is transformed to nonlinear ordinary differential…
Simulations of plasma turbulence in a linear plasma device configuration are presented. These simulations are based on a simplified version of the gyrokinetic (GK) model proposed by B. J. Frei et al. [J. Plasma Phys. 86, 905860205 (2020)]…
This work deals with the numerical solution of the Vlasov equation. This equation gives a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation for the computation of the self-consistent electric field.…
Kinetic models provide highly accurate descriptions of plasma waves but involve complex integrals that are computationally expensive to solve. To facilitate a fluid-like treatment of the system, we propose rational approximations for both…
We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solved for the acoustic particle velocity, mass density, and…
In this paper, we present three-dimensional (3D) Particle-In-Cell (PIC) simulations to study the stability of 2D Bernstein-Greene-Kruskal (BGK) modes in a magnetized plasma with a finite background magnetic field. The simulations were…
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…