Nonautonomous k-contact field theories

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.

27 pp

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Cited by in corpus (5)

• Symmetries, conservation and dissipation in time-dependent contact systems
• Contact Lie systems
• The Herglotz variational principle for dissipative field theories
• Practical Introduction to Action-Dependent Field Theories
• Brackets in multicontact geometry and multisymplectization