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 ...

We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified LagrangianHamiltonian formalism to these kinds of systems. This model provides a straightforward ...

This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” Hamiltonian approach using canonical transformations ...