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 …
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 …
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) …
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 …
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 Page 1 On Long-Time Asymptotics for the Toda Lattice and Its Hamiltonian Perturbations by Deniz Bilman …
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 …