A relation between k-symplectic and k-contact Hamiltonian systems

Systems of partial differential equations which appear in classical field theories can be studied geometrically using different geometrical structures, for example, k-symplectic geometry, k-cosymplectic geometry, multisymplectic geometry, etc. In recent years, there has been a notable increase in the study of k-contact Hamiltonian systems. These are based on the description of the dynamics of field theories using the so-called k-contact manifolds. Such structures are generalizations of contact structures and k-symplectic structures. The relation between k-symplectic manifolds and k-contact manifolds was previoustly established. In light of the above relation, this work seeks to explore the relationship between k-symplectic Hamiltonian systems and k-contact Hamiltonian systems.