We report on the first results of self-consistent second order metric perturbations produced by a point particle moving in the Schwarzschild spacetime. The second order waveforms satisfy a wave equation with an effective source term build up from products of first order metric perturbations and its derivatives. We have explicitly regularized this source term at the particle location as well as ...

The well known Eckart’s singular s−wave potential is PT −symmetrically regularized and continued to the whole real line. The new model remains exactly solvable and its bound states remain proportional to Jacobi polynomials. Its real and discrete spectrum exhibits several unusual features. PACS 03.65.Ge, 03.65.Fd A deeper understanding of one-dimensional systems may be mediated by an analytic co...

We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term. Crank-Nicolson nonlinear-implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energy method. Numerical simu...

A new integral transform method for regularized long-wave (RLW) models having fractional-order is presented in this study. Although analytical approaches are challenging to apply such models, semianalytical or numerical techniques have received much attention the literature. We propose a technique combining transformation, Elzaki (ET), and it equations The RLW describe ion-acoustic waves plasma...

The symmetric regularized long wave system (SRLW) is a model for weakly nonlinear ion acoustic and space-charge waves, introduced by C. Seyler D. Fenstermacher. In this paper, we investigate the Wellposedness controllability properties of generalized (g-SRLW) in different structures, such as periodic bounded domains. Firstly, obtain exact results both linear g-SRLW posed on one-dimensional toru...

The long-time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third-order dispersion is considered by use of Whitham averaging. Under modest assumptions, the jump conditions (DSW locus and speeds) for admissible, weak DSWs are characterized and found to depend only upon the sign of dispersion (conv...

Dissipationless hydrodynamics regularized by dispersion describe a number of physical media including water waves, nonlinear optics, and Bose–Einstein condensates. As in the classical theory of hyperbolic equations where a nonconvex flux leads to nonclassical solution structures, a nonconvex linear dispersion relation provides an intriguing dispersive hydrodynamic analogue. Here, the fifth orde...

We consider an initial boundary-value problem for the Regularized Long Wave equation. A three level conservative difference scheme is studied. On the first level a two level scheme is used to find the values of the unknown functions which ensures the expression of the initial energies only by the initial data. The obtained algebraic equations are linear with respect to the values of the unknown...