Symbolic computation, Bنcklund transformation and analytic N-soliton-like solution for a nonlinear Schrِdinger equation with nonuniformity term from certain space/laboratory plasmas

With symbolic computation, a bilinear Bäcklund transformation is presented for a nonlinear Schrödinger equation with nonuniformity term from certain space/laboratory plasmas, and correspondingly the one-soliton-like solution is derived from the Bäcklund transformation. Simultaneously, the N-soliton-like solution in double Wronskian form is also given. Besides, the authors verify that the ( N − 1 ) - and N-soliton-like solutions satisfy the Bäcklund transformation. The results obtained in this paper might be valuable for the study of the nonuniform media.