Relay-Zone Technique for Numerical Boundary Treatments in Simulating Dark Solitons

摘要： To simulate dark solitons in the defocusing nonlinear Schr?dinger equation, we introduce a relay-zone technique, by alternately using a Robin boundary condition to treat the nonzero far field, and a derivative boundary condition to match the dark soliton. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment. Stability and interaction of dark solitons are also studied.