Symmetries, psudosymmetries and conservation laws in Lagrangian and Hamiltonian $k$-symplectic formalisms

TL;DR

This paper introduces new conservation laws in $k$-symplectic formalisms by extending symmetry concepts to pseudosymmetries, bypassing traditional Noether theorems.

Contribution

It defines pseudosymmetries within $k$-symplectic formalisms and derives novel conservation laws without relying on Noether's theorem.

Findings

New conservation laws for $k$-symplectic systems

Extension of symmetry concepts to pseudosymmetries

Conservation laws derived without Noether's theorem

Abstract

In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for $k$-symplectic Hamiltonian systems and $k$-symplectic Lagrangian systems.