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 …

We prove L 2 orbital stability of Dirac solitons in the massive Thirring model. Our method
uses local well posedness of the massive Thirring model in L 2, conservation of the charge …

We consider the massive Thirring model in the laboratory coordinates and explain how the
inverse scattering transform can be developed with the Riemann–Hilbert approach. The key …

Several integrable semi-discretizations are known in the literature for the massive Thirring
system in characteristic coordinates. We present for the first time an integrable semi …

We consider the massive Thirring model and establish pointwise long-time behavior of its
solutions in weighted Sobolev spaces. For soliton-free initial data we can show that the …

We prove global well-posedness for the coupled Maxwell-Dirac-Thirring-Gross-Neveu
equations in one space dimension, with data for the Dirac spinor in the critical space $ L^ 2 …

This paper studies the strong convergence of the quantum lattice Boltzmann (QLB) scheme
for the nonlinear Dirac equations for Gross-Neveu model in 1+ 1 dimensions. The initial data …

We address a general system of nonlinear Dirac equations in (1+ 1) dimensions and prove
nonexistence of self-similar blowup solutions in the space of bounded functions. While this …

This paper reviews recent mathematical progresses made on the study of the initial-value
problem for nonlinear Dirac equations in one space dimension. We also prove the global …

LARGE TIME BEHAVIOR OF SOLUTION TO NONLINEAR DIRAC EQUATION IN 1+1
DIMENSIONS∗ Page 1 Acta Mathematica Scientia, 2019, 39B(2): 597–606 https://doi.org/10.1007/s10473-019-0221-7 …