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Rogue waves observed in the ocean and elsewhere are often modelled by certain solutions of the nonlinear Schrodinger equation, describing the modulational instability of a plane wave and the subsequent development of multi-phase nonlinear wavetrains. In this paper, we describe how integrability and application of the inverse scattering transform can be used to construct a class of explicit asymptotic solutions which describe this process. We discuss the universal mechanism of the onset ofdoi:10.1098/rspa.2013.0094 fatcat:cjezclb3enfaji3vt3rkkzln7i