7 citations · 9 across the 2 of their papers we have counts for
5 papers
Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime
Deniz Bilman, Peter D. Miller
We study fundamental rogue-wave solutions of the focusing nonlinear Schrödinger equation in the limit that the order of the rogue wave is large and the independent variables $(x,t)…
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…
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…
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…
A robust inverse scattering transform for the focusing nonlinear Schrödinger equation
Deniz Bilman, Peter D. Miller
We propose a modification of the standard inverse scattering transform for the focusing nonlinear Schrödinger equation (also other equations by natural generalization) formulated w…