Exact soliton solutions for a family of<b><i>N</i></b>coupled nonlinear Schrödinger equations in optical fiber media

Abstract

We consider a family of both homogeneous and inhomogeneous N-coupled nonlinear Schr\"odinger equations which govern simultaneous propagation of N fields in an optical fiber with various important physical effects. The eigenvalue problem associated with homogeneous equations is constructed with the help of the Ablowitz-Kaup-Newell-Segur method. Using the B\"acklund transformation method, one-soliton solutions are explicitly derived.