| Abstract: |
| It was shown in the 1960s by Talanov that there exist solutions of the dispersionless focusing nonlinear Schr\odinger equation with a parabolic amplitude profile that collapse and blow up in finite time. Accounting for the effect of small dispersion, Suleimanov conjectured in 2017 that the corresponding solution of the nonlinear Schr\odinger equation should be regularized with a particular wave profile that was later characterized as a certain infinite-order limit of fundamental rogue waves. We describe a recent proof of a version of Suleimanov's conjecture and explain how it generalizes to the full AKNS hierarchy. |
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