Deniz Bilman
Deniz Bilman
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Riemann-Hilbert problems
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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Numerical inverse scattering for the Toda lattice
We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated …
Deniz Bilman
,
Thomas Trogdon
January, 2017
Communications in Mathematical Physics
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