Hamilton-Jacobi theory in k-cosymplectic field theories

TL;DR

This paper extends Hamilton-Jacobi theory to classical field theories within the k-cosymplectic geometric framework, broadening its applicability beyond time-dependent mechanics.

Contribution

It introduces a geometric Hamilton-Jacobi formalism tailored for k-cosymplectic classical field theories, expanding the theoretical foundation.

Findings

Developed a Hamilton-Jacobi formalism for k-cosymplectic field theories

Unified geometric approach for classical field theories and mechanics

Potential applications in solving field equations geometrically

Abstract

In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for time dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.