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Multipulses of Nonlinearly Coupled Schrödinger Equations

✍ Scribed by Alice C. Yew

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
338 KB
Volume
173
Category
Article
ISSN
0022-0396

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✦ Synopsis

The capacity of coupled nonlinear Schro dinger (NLS) 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 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. Conditions for the existence of multipulses, as well as a description of their geometry, are derived from the analysis.

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