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This paper has been published in Physica D. To download a preprint of this paper just click here.

This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-2108029 (Bilman) and DMS-1812625 (Miller). Any opinions, findings and conclusions or recomendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

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Broader Universality of Rogue Waves of Infinite Order

Deniz Bilman and Peter D. Miller

DB: Department of Mathematical Sciences, University of Cincinnati
PDM: Department of Mathematics, University of Michigan, Ann Arbor

Abstract:

We show that the same special solution of the focusing nonlinear Schrödinger 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 Bäcklund transformations.