Broader Universality of Rogue Waves of Infinite Order

TL;DR

This paper demonstrates that a particular rogue wave solution of the focusing nonlinear Schrödinger equation appears universally from any background through iterated Bäcklund transformations, revealing broader universality of infinite-order rogue waves.

Contribution

It introduces a new universal mechanism for generating rogue waves of infinite order from arbitrary backgrounds using Bäcklund transformations.

Findings

The special rogue wave solution arises universally from arbitrary backgrounds.

Iterated Bäcklund transformations generate infinite-order rogue waves.

The approach unifies different rogue wave solutions under a common framework.

Abstract

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