  In this paper, we develop a high order semi-Lagrangian (SL) discontinuous
Galerkin (DG) method for nonlinear Vlasov-Poisson (VP) simulations without
operator splitting. In particular, we combine two recently developed novel
techniques: one is the high order non-splitting SLDG transport method [Cai, et
al., J Sci Comput, 2017], and the other is the high order characteristics
tracing technique proposed in [Qiu and Russo, J Sci Comput, 2017]. The proposed
method with up to third order accuracy in both space and time is locally mass
conservative, free of splitting error, positivity-preserving, stable and robust
for large time stepping size. The SLDG VP solver is applied to classic
benchmark test problems such as Landau damping and two-stream instabilities for
VP simulations. Efficiency and effectiveness of the proposed scheme is
extensively tested. Tremendous CPU savings are shown by comparisons between the
proposed SL DG scheme and the classical Runge-Kutta DG method.
