On the Asymptotic Stability of -Soliton Solutions of the Defocusing Nonlinear Schrödinger Equation

S Cuccagna, R Jenkins - Communications in Mathematical Physics, 2016 - Springer
We consider the Cauchy problem for the defocusing nonlinear Schrödinger (NLS) equation
for finite density type initial data. Using the ∂∂¯ generalization of the nonlinear steepest …

Numerical inverse scattering for the Toda lattice

D Bilman, T Trogdon - Communications in Mathematical Physics, 2017 - Springer
We present a method to compute the inverse scattering transform (IST) for the famed Toda
lattice by solving the associated Riemann–Hilbert (RH) problem numerically. Deformations …

On asymptotic stability of N-solitons of the defocusing nonlinear Schrodinger equation

S Cuccagna, R Jenkins - arXiv preprint arXiv:1410.6887, 2014 - arxiv.org
We consider the Cauchy problem for the Gross-Pitaevskii (GP) equation. Using the DBAR
generalization of the nonlinear steepest descent method of Deift and Zhou we derive the …

Benchmarking numerical methods for lattice equations with the Toda lattice

D Bilman, T Trogdon - Applied Numerical Mathematics, 2019 - Elsevier
We compare the performance of well-known numerical time-stepping methods that are
widely used to compute solutions of the doubly-infinite Fermi–Pasta–Ulam–Tsingou (FPUT) …

Discrete integrable systems, Darboux transformations, and Yang–Baxter maps

D Bilman, S Konstantinou-Rizos - … Notes of the Abecederian School of …, 2017 - Springer
This chapter is devoted to the integrability of discrete systems and their relation to the theory
of Yang–Baxter (YB) maps. Lax pairs play a significant role in the integrability of discrete …

Ranking with hamiltonian dynamics

WG Mitchener - Physica D: Nonlinear Phenomena, 2020 - Elsevier
In data science, a ranking or linear ordering problem is to place items into a linear order
based on comparison data. In this article, we consider a Hamiltonian system, in which …

On long-time asymptotics for the Toda lattice and its Hamiltonian perturbations

D Bilman - 2015 - search.proquest.com
On Long-Time Asymptotics for the Toda Lattice and Its Hamiltonian Perturbations Page 1 On
Long-Time Asymptotics for the Toda Lattice and Its Hamiltonian Perturbations by Deniz Bilman …

Nekhoroshev Stability for the Dirichlet Toda Lattice

A Henrici - Symmetry, 2018 - mdpi.com
In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet
boundary conditions, ie, with fixed ends. The Toda lattice is a member of the family of Fermi …