Bäcklund transformation in bilinear form for a higher-order nonlinear Schrödinger equation

Abstract

Bäcklund transformation in bilinear form is presented for a higher-order nonlinear Schrödinger equation, which describes the propagation of ultrashort light pulses in optical fibers. With symbolic computation and starting from the Bäcklund transformation, the analytical soliton solution is obtained from a trivial solution and the inverse scattering transform scheme is also derived. Furthermore, the N -soliton solution in double Wronskian form is given, and the value of the arbitrary constant appearing in the Bäcklund transformation is determined for a transformation between the ( N − 1 ) and N -soliton solutions. The results obtained from the Bäcklund transformation might be valuable in optical communications.