Korteweg-de Vries equation, Toda lattice and their relevance to the FPUT problem

School of Mathematics and Physics, University of Lincoln

26 May 2021

About the meeting

This one-day meeting aims to highlight aspects of integrable systems theory applied to near-integrable many-body dynamical systems. It will focus on the integrable-like behaviour of the Fermi-Pasta-Ulam-Tsingou (FPUT) model and its relevance with two integrable models, namely the Korteweg-de Vries equation, which describes waves on shallow water surfaces, and the Toda lattice.

The celebrated Fermi-Pasta-Ulam-Tsingou model is a long chain of coupled nonlinear oscillators representing the simplest one-dimensional analogue of atoms in a crystal. This system consists a benchmark in the history of nonlinear science: The FPUT problem sparked the birth of both ‘experimental mathematics’ and integrable systems. Most notably, it is the first dynamical system numerically integrated on a computer while its enigmatic non-ergodic behaviour is puzzling the scientists for over 65 years, with innumerable works published.

The workshop program will consist of talks covering:

  • An introduction to Integrable Systems
  • An overview of FPUT problem
  • The relevance with Korteweg-de Vries equation and the Toda lattice
  • Recent analytical and numerical approaches and progress

Workshop Programme

9:45 – 10:00 Welcome
10:00 – 11:00 Jing Ping Wang (University of Kent)
Integrable systems: what they are and how many?
11:00 – 11:30 Tea/Coffee Break
11:30 – 12:30 Karsten Matthies (University of Bath)
Stability of high-energy travelling waves in FPUT chains
12:30 – 14:00 Lunch Break
14:00 – 15:00 Helen Christodoulidi (University of Lincoln)
Toda observables along FPUT dynamics
15:00 – 16:00 Tamara Grava (University of Bristol & SISSA)
Adiabatic invariants for the FPUT and Toda chains in the thermodynamic limit

Workshop Venue: INB0114 Lecture Theatre, Isaac Newton Building, University of Lincoln, Brayford Pool, University of, Lincoln LN6 7TS or click on the map

Organiser: Helen Christodoulidi

To register to the workshop please fill in the application form found here

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