Painleve analysis of the coupled nonlinear Schrodinger equation for polarized optical waves in an isotropic medium

Using the Painleve analysis, we investigate the integrability properties of a system of two coupled nonlinear Schrodinger equations that describe the propagation of orthogonally polarized optical waves in an isotropic medium. Besides the well-known integrable vector nonlinear Schrodinger equation, we show that there exists a set of equations passing the Painleve test where the self and cross phase modulational terms are of different magnitude. We introduce the Hirota bilinearization and the Backlund transformation to obtain soliton solutions and prove integrability by making a change of variables. The conditions on the third-order susceptibility tensor X-(3) imposed by these integrable equations are explained.