Integrability and singularity structure of coupled nonlinear Schrodinger equations

Multimode propagation of electromagnetic waves in optical fibre is often described by coupled nonlinear Schrodinger (NLS) equations. To understand the integrability properties of such coupled NLS systems, we extend the Painleve singularity structure analysis of two coupled systems to three coupled systems and identify four integrable sets of parameters. We bilinearize these cases to obtain soliton solutions. The results are extended to N-coupled systems, completing the earlier analysis of Sahadevan, Tamizhmani and Lakshmanan.