Painléve Analysis and Backlund Transformations for Coupled Generalized Schrödinger–Boussinesq System

Painléve analysis of coupled generalized Schrödinger–Boussinesq system with arbitrary parameters has been carried out. We identify two branches of leading singularities in the Painléve formalism for PDEs as developed by Weiss et al., [J. Math. Phys, 24, 522 (1983) ] . The coupled system is shown to be completely integrable in one of the branches, for which case the associated Bäcklund transformation is explicitly given. Relevance of the results for coupled nonlinear wave propagation in magnetized plasmas is pointed out.