Variational first-order partial differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:191

Article

Haková, A ; Krupková, O

关键词: first-order partial differential equations;    Lagrangian;    closed form;    differential ideal;    Hamiltonian system;    multisymplectic form;   

DOI  :  10.1016/S0022-0396(02)00160-2

来源: Elsevier

【 摘 要 】

Geometrical and variational properties of systems of first-order partial differential equations (PDE) on fibered manifolds are studied. Existence of Lagrangians is shown to be equivalent with the existence of a closed form which is global and unique; an explicit construction of this form is given. A bijective map between a set of dynamical forms on J(1) Y, representing first-order PDE, and forms on the total space Y is found, providing a geometric description of the equations by means of a (not necessarily closed) ideal generated by a system of n-forms on Y (n = dimension of the base manifold). Conditions for this ideal to be closed are studied. Relations with Hamiltonian structures and with multisymplectic forms are discussed. (C) 2002 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free