Separable graph Hamiltonian network: A graph deep learning model for lattice systems

R Geng, J Zu, Y Gao, HK Zhang - Physical Review Research, 2024 - APS
Addressing the challenges posed by nonlinear lattice models, which are vital across diverse
scientific disciplines, we present a new deep learning approach that harnesses the power of …

Graph Attention Hamiltonian Neural Networks: A Lattice System Analysis Model Based on Structural Learning

R Geng, Y Gao, J Zu, HK Zhang - arXiv preprint arXiv:2412.10821, 2024 - arxiv.org
A deep understanding of the intricate interactions between particles within a system is a key
approach to revealing the essential characteristics of the system, whether it is an in-depth …

Continuation of spatially localized periodic solutions in discrete NLS lattices via normal forms

V Danesi, M Sansottera, S Paleari, T Penati - Communications in Nonlinear …, 2022 - Elsevier
We consider the problem of the continuation with respect to a small parameter ɛ of spatially
localized and time periodic solutions in 1-dimensional dNLS lattices, where ɛ represents the …

On the continuation of degenerate periodic orbits via normal form: Lower dimensional resonant tori

M Sansottera, V Danesi, T Penati, S Paleari - Communications in Nonlinear …, 2020 - Elsevier
We consider the classical problem of the continuation of periodic orbits surviving to the
breaking of invariant lower dimensional resonant tori in nearly integrable Hamiltonian …

Low dimensional completely resonant tori in Hamiltonian Lattices and a Theorem of Poincaré

T Penati, V Danesi, S Paleari - Mathematics in Engineering, 2021 - air.unimi.it
We present an extension of a classical result of Poincaré (1892) about continuation of
periodic orbits and breaking of completely resonant tori in a class of nearly integrable …

Revisiting multi-breathers in the discrete Klein–Gordon equation: a spatial dynamics approach

R Parker, J Cuevas-Maraver, PG Kevrekidis… - …, 2022 - iopscience.iop.org
We consider the existence and spectral stability of multi-breather structures in the discrete
Klein–Gordon equation, both for soft and hard symmetric potentials. To obtain analytical …

Periodic and quasi-periodic orbits in nearly integrable Hamiltonian systems

V Danesi - 2021 - air.unimi.it
The study of periodic and quasi-periodic orbits in nearly integrable Hamiltonian systems is a
long standing and challenging problem, that dates back to Poincaré. Quoting Poincaré, they …