Second-order integrable Lagrangians and WDVV equations

被引：2
作者：
Ferapontov, E. V. [1 ,2 ]
Pavlov, M. V. [3 ]
Xue, Lingling [3 ]
机构：
[1] Loughborough Univ, Dept Math Sci, Loughborough LE11 3TU, Leics, England
[2] Russian Acad Sci, Inst Math, Ufa Fed Res Ctr, 112 Chernyshevsky St, Ufa 450008, Russia
[3] Ningbo Univ, Dept Appl Math, Ningbo 315211, Peoples R China
来源：
LETTERS IN MATHEMATICAL PHYSICS | 2021年 / 111卷 / 02期
基金：
中国国家自然科学基金; 英国工程与自然科学研究理事会;
关键词：
Second-order Lagrangians; Systems of hydrodynamic type; Integrability (diagonalisability) conditions; Jacobi theta functions; Chazy equation; WDVV equations; HYDRODYNAMIC TYPE; SYSTEMS; GEOMETRY;
D O I：
10.1007/s11005-021-01403-3
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We investigate the integrability of Euler-Lagrange equations associated with 2D second-order Lagrangians of the form integral f (u(xx), u(xy), u(yy)) 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. Alink of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.
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页数：33
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