Extreme, or “rogue,” waves are those in the tail of the probability distribution and are a matter of great concern and considerable research. They may be partly associated with non-Gaussian behavior caused by resonant nonlinear interactions. Here it is shown that even in a Gaussian sea, “unexpected” waves, in the sense of, for example, waves twice as large as any in the preceding 30 periods, oc...

We show that the same special solution of focusing nonlinear Schr\"{o}dinger equation has been shown to arise in a certain near-field/large-order limit from soliton and Peregrine-like rogue wave solutions actually arises universally an arbitrary background when subjected sequence iterated B\"{a}cklund transformations.

Abstract