Deniz Bilman
Deniz Bilman
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nonlinear Schrödinger equation
Extreme superposition: High-order fundamental rogue waves in the far-field regime
We study fundamental rogue-wave solutions of the focusing nonlinear Schrödinger equation in the limit that the order of the rogue wave …
Deniz Bilman
,
Peter D. Miller
April, 2022
in press
,
Memoirs AMS
ArXiv
Broader universality of rogue waves of infinite order
We show that the same special solution of the focusing nonlinear Schrödinger equation that has been shown to arise in a certain …
Deniz Bilman
,
Peter D. Miller
March, 2022
Physica D
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Far-field asymptotics for multiple-pole solitons in the large-order limit
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair …
Deniz Bilman
,
Robert Buckingham
,
Deng-Shan Wang
January, 2021
Journal of Differential Equations
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Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
We analyze the large-$n$ behavior of soliton solutions of the integrable focusing nonlinear Schrödinger equation with associated …
Deniz Bilman
,
Robert Buckingham
April, 2019
Journal of Nonlinear Science
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Extreme superposition: Rogue waves of infinite order and the Painlevé-III hierarchy
We study the fundamental rogue wave solutions of the focusing nonlinear Schrödinger equation in the limit of large order. Using a …
Deniz Bilman
,
Liming Ling
,
Peter D. Miller
August, 2018
Duke Mathematical Journal
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A robust inverse scattering transform for the focusing nonlinear Schrödinger equation
We propose a modification of the standard inverse scattering transform for the focusing nonlinear Schrödinger equation (also other …
Deniz Bilman
,
Peter D. Miller
October, 2017
Communications on Pure and Applied Mathematics
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