Painleve analysis and integrability of coupled non-linear Schrodinger equations

Abstract

Considering a system of coupled non-linear Schrodinger (NLS) equations, the authors discuss the integrability properties through Painleve (P) analysis. For the two coupled NLS equations, they show that there exists a pair of parametric values possessing the P property, for which the associated Backlund transformation (BT) and the Hirota bilinearisation are constructed. These parametric choices are identical to those of Zakharov and Schulman (1982) who established the integrability in terms of 'motion invariants'. Finally, they extend the P analysis to the N coupled NLS system, and identify two parametric choices possessing the P property, which are natural generalisations of the two coupled NLS cases.