Abstract: The one-soliton solution of the nonlinear Schrdinger equation with an external potential of the form of V(x,t) =f1(t)x+f2(t)x2 is examined.It is shown that,while the center of the soliton obeys Newton’s equation with the potential V(x,t),the internal structure of the soliton is determined by the NLSE of the "body-fixed" coordinate system.The soliton structure is found to be independent of f1(t).In principle,the soliton can be diffused if f2(t) varies rapidly.Through numerical method,however,that the soliton is extremely tenacious against rapid variations of f2(t).