On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory

TL;DR

This paper explores specific Noether symmetries in k-cosymplectic Hamiltonian systems within classical field theories and extends Noether's theorem to associate conservation laws with these symmetries.

Contribution

It introduces a new class of symmetries in k-cosymplectic systems and generalizes Noether's theorem to link these symmetries with conservation laws.

Findings

Identification of a particular class of symmetries in k-cosymplectic systems

Development of a generalized Noether's theorem for these symmetries

Establishment of a method to derive conservation laws from the symmetries

Abstract

This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating conservation laws to them by means of a suitable generalization of Noether's theorem.