In this paper, we consider the multi-symplectic Runge–Kutta (MSRK) methods applied to the
nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi …

We present several numerical methods and establish their error estimates for the
discretization of the nonlinear Dirac equation (NLDE) in the nonrelativistic limit regime …

We consider in this paper spectral and pseudospectral approximations using Hermite
functions for PDEs on the whole line. We first develop some basic approximation results …

This paper presents a review of the current state-of-the-art of numerical methods for
nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+ 1) …

In this work, we consider the numerical integration of the nonlinear Dirac equation and the
Dirac–Poisson system (NDEs) under rough initial data. We propose an ultra low-regularity …

A $\mathcal {PT} $-symmetric nonlinear Schr\" odinger dimer is a two-site discrete nonlinear
Schr\" odinger equation with one site losing and the other one gaining energy at the same …

The present situation of the classical theory of nonlinear Dirac fields and, specially, of its
particle-like solutions is reviewed. The emphasis is placed on a line of research which …

A finite difference scheme is presented for the Dirac equation in (1+ 1) D. It can handle
space-and time-dependent mass and potential terms and utilizes exact discrete transparent …

We consider the nonlinear Dirac equation in 1+ 1 dimension with scalar-scalar self
interaction g 2 κ+ 1 (Ψ¯ Ψ) κ+ 1 and with mass m. Using the exact analytic form for rest frame …

Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make
a variety of practical applications. We here start with the recent idea of nonlinear QW and …