Internal Lagrangians of PDEs as variational principles

被引：1

作者：

Druzhkov, Kostya ^{[1
]}

机构：

[1] Russian Armenian Univ, 123 Hovsep Emin St, Yerevan 0051, Armenia

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2024年 / 199卷

关键词：

Variational principle; Presymplectic structure; Noether's theorem; Internal Lagrangian; FORMALISM; CALCULUS;

D O I：

10.1016/j.geomphys.2024.105143

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between symmetries, conservation laws and internal Lagrangians is established. Noether's theorem is formulated in terms of internal Lagrangians. A relation between non-degenerate Lagrangians and the corresponding internal Lagrangians is investigated. Several examples are discussed. (c) 2024 Elsevier B.V. All rights reserved.

引用

页数：18

共 20 条

[1] Crnkovic C., 1986, 300 YEARS GRAVITATIO, V676
[2] Dorfman I., 1993, NONLINEAR SCI THEORY
[3] Extendable symplectic structures and the inverse problem of the calculus of variations for systems of equations written in generalized Kovalevskaya form
Druzhkov, K. P.
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2021, 161
[4] Lagrangian formalism and the intrinsic geometry of PDEs
Druzhkov, Kostya
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2023, 189
[5] On relativistic wave equations for particles of arbitrary spin in an electromagnetic field
Fierz, M
Pauli, W
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1939, 173 (A953) : 0211 - 0232
[6] Gotay M. J., 1991, Differential Geometry and its Applications, V1, P375, DOI 10.1016/0926-2245(91)90014-Z
[7] Grigoriev M, 2016, Arxiv, DOI arXiv:1606.07532
[8] Presymplectic structures and intrinsic Lagrangians for massive fields
Grigoriev, Maxim
Gritzaenko, Vyacheslav
[J]. NUCLEAR PHYSICS B, 2022, 975
[9] Hélein F, 2004, ADV THEOR MATH PHYS, V8, P565
[10] ON THE INVERSE PROBLEM OF THE CALCULUS OF VARIATIONS IN FIELD-THEORY
HENNEAUX, M
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1984, 17 (01): : 75 - 85

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