Multipulses of nonlinearly coupled Schrodinger equations

The capacity of coupled nonlinear Schrodinger (NLS) equations to support mu ltipulse solutions (multibump solitary-waves) is investigated. A detailed a nalysis is undertaken for a system of quadratically coupled equations that describe the phenomena of second harmonic generation and parametric wave in teraction in non-centrosymmetric optical materials. Utilising ihc framework of homoclinic bifurcation theory. and employing a Lyapunov-Schmidt reducti on method developed by Hale. Lin. and Sandstede, a novel mechanism for the generation of multipulses is identified. which arises from a resonant semi- simple eigenvalue configuration of the linearised steady-state equations. C onditions for the existence of multipulses. as well as a description of the ir geometry, are derived from thc analysis. (C) 2001 Academic Press.