101 citations · 322 across the 12 of their papers we have counts for
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math.AP2018
On numerical inverse scattering for the Korteweg-de Vries equation with discontinuous step-like data
Deniz Bilman, Thomas Trogdon
We present a method to compute dispersive shock wave solutions of the Korteweg-de Vries equation that emerge from initial data with step-like boundary conditions at infinity. We de…
nlin.SI2018★ 79 cited
Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
Deniz Bilman, Robert Buckingham
We analyze the large- behavior of soliton solutions of the integrable focusing nonlinear Schrödinger equation with associated spectral data consisting of a single pair of conjug…
nlin.SI2018★ 101 cited
Extreme Superposition: Rogue Waves of Infinite Order and the Painlevé-III Hierarchy
Deniz Bilman, Liming Ling, Peter D. Miller
We study the fundamental rogue wave solutions of the focusing nonlinear Schrödinger equation in the limit of large order. Using a recently-proposed Riemann-Hilbert representation o…