Related papers: The periodic standing-wave approximation: nonlinea…
In the present work, we introduce a new $\mathcal{PT}$-symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
This study employs spectral methods to capture the behaviour of wave equation with dispersive-nonlinearity. We describe the evolution of hump initial data and track the conservation of the mass and energy functionals. The…
Nonlinear electrodynamics model in hypercomplex form is considered. Its linearization around a solution is obtained. The appropriate problem for linear waves around static dyon solution (SDS) of Born-Infeld electrodynamics is investigated.…
In magnetized plasmas of fusion devices the strong magnetic field leads to highly anisotropic physics where solution scales along field lines are much larger than perpendicular to it. Hence, regarding both accuracy and efficiency, a…
In this paper, we present an accurate numerical method for the time-harmonic Maxwell's equations for bi-periodic multilayered media with quasi-periodic incident waves using the Method of Fundamental Solutions in conjunction with a…
We consider standing waves with frequency $\omega$ for 4-superlinear Schr\"odinger-Poisson system. For large $\omega$ the problem reduces to a system of elliptic equations in $\mathsf{R}^3$ with potential indefinite in sign. The variational…
In this paper, we study a non-integrable discrete lattice model which is a variant of an integrable discretization of the standard Hopf equation. Interestingly, a direct numerical simulation of the Riemann problem associated with such a…
In this paper, we study the nonlinear dispersive waves including the rarefaction and dispersive shock waves in the discrete modified KdV equation through the numerical simulations of the dispersive Riemann problems. In particular, we…
We present an explicit solver of the three-dimensional screened and unscreened Poisson's equation which combines accuracy, computational efficiency and versatility. The solver, based on a mixed plane-wave / interpolating scaling function…
This paper investigates the application of a fast-wave slow-wave spectral deferred correction time-stepping method (FWSW-SDC) to the compressible Euler equations. The resulting model achieves arbitrary order accuracy in time, demonstrating…
In this paper we propose an accurate, and computationally efficient method for incorporating adaptive spatial resolution into weakly-compressible Smoothed Particle Hydrodynamics (SPH) schemes. Particles are adaptively split and merged in an…
The Schwarz Waveform Relaxation algorithm (SWR) exchanges the waveform of boundary value between neighbouring sub-domains, which provides a more efficient way than the other Schwarz algorithms to realize distributed computation. However,…
Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions…
We consider existence and stability properties of nonlinear spatially periodic or quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic oscillators. Specifically, we consider Klein-Gordon (KG) chains with…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation…
Numerical relativity has traditionally been pursued via finite differencing. Here we explore pseudospectral collocation (PSC) as an alternative to finite differencing, focusing particularly on the solution of the Hamiltonian constraint (an…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
The Whitham equation is a nonlocal, nonlinear partial differential equation that models the temporal evolution of spatial profiles of surface displacement of water waves. However, many laboratory and field measurements record time series at…