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An explanation is given for previous numerical results which suggest acertain bifurcation of `vector solitons' from scalar (single-component)solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcationin question is nonlocal in the sense that the vector soliton does not have asmall-amplitude component, but instead approaches a solitary wave of onecomponent with two infinitely far-separated waves in the other component. Yet,it is argued that this highly nonlocal event can be predicted from a purelylocal analysis of the central solitary wave alone. Specifically thelinearisation around the central wave should contain asymptotics which grow atprecisely the speed of the other-component solitary waves on the two wings.This approximate argument is supported by both a detailed analysis based onmatched asymptotic expansions, and numerical experiments on two examplesystems. The first is the usual coupled NLS system involving an arbitrary ratiobetween the self-phase and cross-phase modulation terms, and the second is acoupled NLS system with saturable nonlinearity that has recently beendemonstrated to support stable multi-peaked solitary waves. The asymptoticanalysis further reveals that when the curves which define the proposedcriterion for scalar nonlocal bifurcations intersect with boundaries of certainlocal bifurcations, the nonlocal bifurcation could turn from scalar tonon-scalar at the intersection. This phenomenon is observed in the firstexample. Lastly, we have also selectively tested the linear stability ofseveral solitary waves just born out of scalar nonlocal bifurcations. We foundthat they are linearly unstable. However, they can lead to stable solitarywaves through parameter continuation.Comment: To appear in Nonlinearit

A scalar nonlocal bifurcation of solitary waves for coupled nonlinear Schr dinger systems