Motion of solitons in one-dimensional spin-orbit-coupled Bose-Einstein   condensates
  Solitons play a fundamental role in dynamics of nonlinear excitations. Here we explore the motion of solitons in one-dimensional uniform Bose-Einstein condensates subjected to a spin-orbit coupling (SOC). We demonstrate that the spin dynamics of solitons is governed by a nonlinear Bloch equation. The spin dynamics influences the orbital motion of the solitons leading to the spin-orbit effects in the dynamics of the macroscopic quantum objects (mean-field solitons). The latter perform oscillations with a frequency determined by the SOC, Raman coupling, and intrinsic nonlinearity. These findings reveal unique features of solitons affected by the SOC, which is confirmed by analytical considerations and numerical simulations of the underlying Gross-Pitaevskii equations. 
Lin Wen, Q. Sun, Yu Chen, Deng-Shan Wang, J. Hu, H. Chen, W.-M. Liu,   G. Juzeli\=unas, Boris A. Malomed and An-Chun Ji
cond-mat.quant-gas nlin.PS