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It is well known that k-contact geometry is a suitable framework to deal withnon-conservative field theories. In this paper, we study some relations betweensolutions of the k-contact Euler-Lagrange equations, symmetries, dissipationlaws and Newtonoid vector fields. We review the k-contact Euler-Lagrangeequations written in terms of k-vector fields and sections and provide newresults relating the solutions in both approaches. We also study different kindof symmetries depending on the structures they preserve: natural (preservingthe Lagrangian function), dynamical (preserving the solutions), and k-contact(preserving the underlying geometric structures) symmetries. For some of thesesymmetries, we provide Noether-like theorems relating symmetries anddissipation laws. We also analyse the relation between k-contact symmetries andNewtonoid vector fields. Throughout the paper, we will use the damped vibratingstring as our main illustrative example.

Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws