Therefore, for the certain class of solutions of generalized GPE ( λ λ = 4 for the true one-dimensional condensate and λ λ = 2 while using the three dimensional equation in one dimension), two equations are one. Furthermore, taking the λ λ = 3 case with the minus sign and the ϕ ϕ real, one obtains an attractive self-interaction that should yield a bright soliton.