Our latest results studying how the Peregrine soliton appears as a universal nonlinear structure have been published in Phys Rev Lett. https://tinyurl.com/y5ntlgwa
There is also an earlier version on arXiv here: http://arxiv.org/abs/1701.08527
Brief Summary. The Peregrine soliton is a seminal solution of the nonlinear Schrödinger equation (NLSE), and although it is widely believed that it is associated only with nonlinear modulation instability, recent theory has shown that it actually appears much more generally as a universal structure emerging locally during nonlinear pulse compression. Our paper quantitatively confirms this theory and firmly establishes the universality of the Peregrine soliton. Our results are of fundamental significance to nonlinear physics, and the ubiquitous nature of the NLSE leads us to expect them to stimulate research in areas such as plasma physics, cold atoms, and hydrodynamics.