Abstract: The theoretical results are presented using the Lagrange approach for matter wave

solitons motion in some external potentials. The focus is the solitons with zero initial

velocity，which exhibit different behaviors in po- tential wells and barriers，and the results are

that the barrier repels solitons and the potential well attracts solitons. These conclusions are

verified by numerical simulation.

Key words: Bose-Einstein condensate, soliton, Lagrangian