Painlevé analysis of the coupled nonlinear Schrödinger equation for polarized optical waves in an isotropic medium

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