We investigate numerically the effect of linear damping on
the collapse of nonlinear waves that propagate in a Kerr
medium. Our principal finding is that for a more comprehensive
model based on the nonlinear Helmholtz equation (NLH) the
collapse is delayed compared to a simpler model based on
the nonlinear Schroedinger equation (NLS). This indicates
that the phenomena of nonparaxiality and backscattering
that are disregarded in the NLS may play a fundamental role
as mechanisms that control the growth of the waves' amplitude
and prevent it from becoming infinite at a finite propagation
distance.
Joint work with Gadi Fibich and Boaz Ilan.
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