rspa.2021.0047.pdf (295.02 kB)
Download file

On a class of integrable Hamiltonian equations in 2+1 dimensions

Download (295.02 kB)
journal contribution
posted on 23.04.2021, 10:23 authored by Ben Gormley, Evgeny FerapontovEvgeny Ferapontov, Vladimir NovikovVladimir Novikov
We classify integrable Hamiltonian equations of the form ut = ∂x (δH/δu ) , H = ò h(u, w) dxdy, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w = ∂ −1 x ∂yu. Based on the method of hydrodynamic reductions, the integrability conditions are derived (in the form of an involutive PDE system for the Hamiltonian density h). We show that the generic integrable density is expressed in terms of the Weierstrass σ-function: h(u, w) = σ(u)e w. Dispersionless Lax pairs, commuting flows and dispersive deformations of the resulting equations are also discussed.

Funding

Challenges of dispersionless integrability: Hirota type equations

Engineering and Physical Sciences Research Council

Find out more...

A novel approach to integrability of semi-discrete systems. EP/V050451/1

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volume

477

Issue

2249

Publisher

The Royal Society Publishing

Version

VoR (Version of Record)

Rights holder

© The authors

Publisher statement

This is an Open Access Article. It is published by the Royal Society under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

Acceptance date

30/04/2021

Publication date

2021-5-26

Copyright date

2021

ISSN

1364-5021

eISSN

1471-2946

Language

en

Depositor

Prof Evgeny Ferapontov. Deposit date: 20 April 2021

Article number

20210047