Multipulses of Nonlinearly-coupled Schrr Odinger Equations

The capacity of coupled nonlinear Schrr odinger equations to support multipulse solutions (multibump solitary-waves) is investigated. A detailed analysis is undertaken for a system of quadratically coupled equations that describe the phenomena of second harmonic generation and parametric wave interaction in non-centrosymmetric optical materials. Utilising the framework of homoclinic bifurcation theory, and employing a Lyapunov-Schmidt reduction method developed by Lin 1] and Sandstede 2], a novel mechanism for the generation of multipulses is identiied, which arises from a resonant semi-simple eigenvalue connguration of the linearised steady-state equations. Conditions for the existence of multipulses, as well as a description of their geometry, are derived from the analysis.