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

TL;DR

This paper explores the relationship between k-symplectic and k-contact Hamiltonian systems, which are geometric frameworks used to study classical field theories and their dynamics.

Contribution

It investigates the connection between k-symplectic and k-contact Hamiltonian systems, extending previous work on their relationship in geometric field theory.

Findings

Established a link between k-symplectic and k-contact Hamiltonian systems.

Provided geometric insights into the dynamics of classical field theories.

Extended the understanding of structures underlying field theory models.

Abstract

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.