In this survey, we review the classical Hamilton–Jacobi theory from a geometric point of view
in different geometric backgrounds. We propose a Hamilton–Jacobi equation for different …

In this paper, we apply the geometric Hamilton–Jacobi theory to obtain solutions of classical
hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As …

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent
and independent. In order to do so, we construct a Hamilton–Jacobi theory for these systems …

This work is devoted to review the modern geometric description of the Lagrangian and
Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” …

In this paper, we develop a Hamilton–Jacobi theory for forced Hamiltonian and Lagrangian
systems. We study the complete solutions, particularize for Rayleigh systems, and present …

A hybrid system is a system whose dynamics are controlled by a mixture of both continuous
and discrete transitions. The geometric framework for the Hamilton-Jacobi theory is …

In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson
manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied …

The geometric framework for the Hamilton-Jacobi theory developed in the studies of
Cariñena et al.[Int. J. Geom. Methods Mod. Phys. 3 (7), 1417–1458 (2006)], Cariñena et …

Many physical systems are described by partial differential equations (PDEs). Determinism
then requires the Cauchy problem to be well-posed. Even when the Cauchy problem is well …

The geometric framework for the Hamilton–Jacobi theory is used to study this theory in the
background of higher-order mechanical systems, in both the Lagrangian and Hamiltonian …