Nonautonomous k-contact field theories

TL;DR

This paper introduces a novel geometric framework called k-cocontact geometry for describing non-conservative field theories with explicit space-time dependence, unifying Hamiltonian and Lagrangian formalisms.

Contribution

It develops the k-cocontact geometric framework, extending previous k-contact formalisms to nonautonomous field theories with explicit space-time dependence.

Findings

Unified Hamiltonian and Lagrangian formalisms for non-conservative fields

Comparison with autonomous k-contact formalism

Application to nonlinear damped wave equation with forcing

Abstract

This paper provides a new geometric framework to describe non-conservative field theories with explicit dependence on the space-time coordinates by combining the k-cosymplectic and k-contact formulations. This geometric framework, the k-cocontact geometry, permits to develop a Hamiltonian and Lagrangian formalisms for these field theories. We also compare this new formulation in the autonomous case with the previous k-contact formalism. To illustrate the theory, we study the nonlinear damped wave equation with external time-dependent forcing.