Nonlinear Waves in a Cigar-Shaped Bose-Einstein Condensate with Dissipation

We discuss the possible nonlinear waves of atomic matter waves in acigar-shaped Bose-Einstein condensate with dissipation. The wavescan be described by a KdV-type equation. The KdV-type equation hasa solitary wave solution. The amplitude, speed, and width ofthe wave vary exponentially with time t. The dissipative termof γ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both arein good agreement.