| Abstract: |
| In 2017, B. Suleimanov identified a particular \emph{isomonodromic} solution of the focusing nonlinear Schr\odinger equation in a study of dispersive regularization of blowup solutions of unstable geometrical optics systems. The same solution was independently found by D. Bilman, L. Ling, and the speaker to describe near-field asymptotics of high-order rogue wave solutions and hence was labeled as the \emph{rogue wave of infinite order}; it also been also shown by Bilman and R. Buckingham to describe high order soliton solutions of the same equation. In this talk, after describing the rogue wave of infinite order, we will give rigorous proof that the solution arises in a setting similar to that in which it was originally proposed by Suleimanov. That proof is joint work with Buckingham and R. Jenkins. |
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