A contact geometry framework for field theories with dissipation

Jordi Gaset; Xavier Gràcia; Miguel C. Muñoz-Lecanda; Xavier Rivas; Narciso Román-Roy

doi:10.1016/j.aop.2020.168092

paper

A contact geometry framework for field theories with dissipation

arXiv:1905.07354 · doi:10.1016/j.aop.2020.168092

Abstract

We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of $k$ -contact structure and $k$ -contact Hamiltonian system. This is a generalization of both the contact Hamiltonian systems in mechanics and the $k$ -symplectic Hamiltonian systems in field theory. The concepts of symmetries and dissipation laws are introduced and developed. Two relevant examples are analyzed in detail: the damped vibrating string and Burgers' equation.

26 pp. Minor corrections. The bibliography has been updated