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Second-order integrable Lagrangians and WDVV equations

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posted on 27.04.2021, 11:10 by Evgeny Ferapontov, Maxim Pavlov, Lingling Xue
We investigate the integrability of Euler-Lagrange equations associated with 2D second-order Lagrangians of the form Z f(uxx, uxy, uyy) dxdy. By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

Funding

Challenges of dispersionless integrability: Hirota type equations

Engineering and Physical Sciences Research Council

Find out more...

Russian Foundation for Fundamental Research (grant 18-51-18007)

National Natural Science Foundation of China (grant numbers: 11501312, 11775121 and 11631007)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Letters in Mathematical Physics

Volume

111

Issue

2

Publisher

Springer

Version

VoR (Version of Record)

Rights holder

© The Authors

Publisher statement

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

Acceptance date

12/04/2021

Publication date

2021-04-26

Copyright date

2021

DOI

ISSN

0377-9017

eISSN

1573-0530

Publisher version

Language

en

Depositor

Prof Evgeny Ferapontov. Deposit date: 12 April 2021

Article number

58

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Second-order integrable Lagrangians and WDVV equations
Loughborough Publications

Categories

Keywords

second-order Lagrangianssystems of hydrodynamic typeintegrability (diagonalisability) conditionsJacobi theta functionsChazy equationWDVV equations

Licence

CC BY 4.0

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