KdV Description of Dark Solitons in Bose-Einstein Condensation (BEC)

A one‐dimensional solitary wave pulse in the superfluid Bose gas under the limiting conditions of unitarity region and BEC region is studied ,based on the mean‐field theory in combination with the proper‐ty of Bose‐Einstein condensation and through the two‐mode approximation .By using the reductive pertur‐bation method ,a (KdV) equation for the nonlinear electron‐acoustic solitary waves is derived ,from which a solitary wave solution is obtained .It is found that the amplitude and width of the solitary waves depend on the parameters c ,c0 ,c1 ,γ,γ0 and γ1 and on the scattering length a .