Abstract
By developing a small amplitude soliton approximation method, we study analytically weak nonlinear excitations in cigar-shaped condensates with repulsive interatomic interaction under consideration of external perturbation potential. It is shown that matter wave solitons may exist and travel over a long distance without attenuation and change in shape by properly adjusting the strength of interatomic interaction to compensate for the effect of external perturbation potential.
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