Related papers: Travelling waves and a fruitful `time' reparametri…
The behaviour of a "test" electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einstein's general relativity. We have expressed the general solution to the de Rham equations as a…
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
Relativistic plasmas are central to the study of black hole accretion, jet physics, neutron star mergers, and compact object magnetospheres. Despite the need to accurately capture the dynamics of these plasmas and the implications for…
In this article, we provide an alternative way to construct small amplitude traveling waves for general Whitham type equations, in both periodic and whole line contexts. More specifically, Fourier analysis techniques allow us to reformulate…
We consider the Vlasov--Poisson system describing a two-species plasma with spatial dimension $1$ and the velocity variable in $\mathbb{R}^n$. We find the necessary and sufficient conditions for the existence of solitary waves, shock waves,…
The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear…
Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by…
We explore the nonlinear response of plasmonic materials driven by ultrashort pulses of electromagnetic radiation with temporal duration of few femtoseconds and high peak intensity. By developing the Fokker-Planck-Landau theory of electron…
The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization…
We derive approximate iterative analytical solutions of the non-extensive Boltzmann transport equation in the relaxation time approximation. The approximate solutions almost overlap with the exact solution for a considerably wide range of…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation…
Electromagnetic waves propagating through vacuum can polarize virtual electron-positron pairs; this polarization, in turn, nonlinearly modifies their propagation. A semi-classical nonlinear wave equation describing the propagation is…
A novel third order nonlinear evolution equation governing the dynamics of high frequency electrostatic drift waves has been derived in the framework of a plasma fluid model in an inhomogeneous magnetized plasma. The linear dispersion…
In plasma physics, collisionless charged particles are transported following the dynamics of a meanfield Vlasov equation with a self-consistent electric field generated by the charge density. Due to the long range interaction between…
A quantum model based on a Euler-Lagrange variational approach is proposed. In analogy with the classical transport, our approach maintain the description of the particle motion in terms of trajectories in a configuration space. Our method…
A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine…
In this paper we study symmetry reductions of a class of nonlinear third order partial differential equations $u_t -\epsilon u_{xxt} +2\kappa u_x= u u_{xxx} +\alpha u u_x +\beta u_x u_{xx}$ where $\epsilon$, $\kappa$, $\alpha$ and $\beta$…
The generation of energetic electrons in laser fusion in an important issue. The electrons may either arise from a laser plasma instability, or from the uncoupled high temperature tail of a Maxwellian distribution. To study these in a laser…