  Single-particle dynamics of a spin-orbit-coupled Bose-Einstein condensate has
recently been investigated in experiments that explore the physics of
Landau-Zener tunneling and of the Zitterbewegung. In this paper, we study the
influence of a nonlinearity due to interactions on these dynamics and show that
the dispersion relation develops interesting loop strucures. The atoms can move
along the nonlinear dispersion curve in the presence of a weak acceleration
force and we show that the loops lead to straightforward nonlinear Landau-Zener
tunneling. However, we find that for the Zitterbewegung, induced by a sudden
quench in the spin-orbit coupling parameters, the nonlinear dispersion is
irrelevant.
