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Unphysical metastability of the fundamental Raman soliton in the reduced nonlinear Schroedinger equation

We demonstrate theoretically and numerically that the fundamental Raman soliton of the widely used nonlinear Schroedinger equation (NLSE) with a linear approximation of the Raman gain ({\em reduced} NLSE) is metastable. It can propagate for hundreds of dispersion lengths along the optical fibre before eventually disappearing due to a peculiar instability, leading to a collapse. The noise eigenfunction analysis agrees well with the results obtained via direct pulse propagation simulations. This instability is not present when modelling the Raman effect via a full convolution, and thus the reduced NLSE often leads to unphysical results, and should be avoided.