Jacobi equation for field theories and a geometric variational description of dissipation

2025/11/05 by David Martı́n de Diego, de Diego, David Martin, Najma Mosadegh +1
Mathematics · Physics and Astronomy · #53D42 #70S05 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2511.03800

openalex publication_date 2025/11/05 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

In this paper we give a geometric description of the Jacobi equations associated to a first-order Lagrangian field theory using a prolongation of the Lagrangian L on a k-cosymplectic formulation. Moreover, using an appropriate modification of the prolonged Lagrangian, we obtain a variational formulation of field theories with dissipation.

Citations

• Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic approaches
• Multisymplectic geometry, variational integrators, and nonlinear PDEs

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