Related papers: Analogs of the Hamilton-Jacobi and Schrodinger Equ…
The covariant Hamilton-Jacobi formulation of Maxwell's equations is derived from the first-order (Palatini-like) Lagrangian using the analysis of constraints within the De~Donder-Weyl covariant Hamiltonian formalism and the corresponding…
In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…
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.
The Hamiltonian counterpart of classical Lagrangian field theory is covariant Hamiltonian field theory where momenta correspond to derivatives of fields with respect to all world coordinates. In particular, classical Lagrangian and…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained…
A generalized Hamilton-Jacobi representation describes microstates of the Schr\"odinger wave function for bound states. At the very points that boundary values are applied to the bound state Schr\"odinger wave function, the generalized…
The real coordinates separating geodesic Hamilton-Jacobi equation on three-dimensional Minkowski space in several cases cannot be defined in the whole space. We show through an example how to naturally extend them to complex variables…
Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…
Hamilton-Jacobi theory for general relativity provides an elegant covariant formulation of the gravitational field. A general `coordinate-free' method of integrating the functional Hamilton-Jacobi equation for gravity and matter is…
Motivated by the Hamilton$-$Jacobi approach of fields with constraints, we analyse the classical structure of three different constrained field systems: (i) the scalar field coupled to two flavors of fermions through Yukawa couplings (ii)…
The Hamilton-Jacobi [$HJ$] analysis for higher-order Chern-Simons gravity is performed. The complete set of $HJ$ Hamiltonians are identified and a fundamental $HJ$ differential is constructed, from which the characteristic equations are…
Multivariable generalizations of the continuous Hahn and Wilson polynomials are introduced as eigenfunctions of rational Ruijsenaars type difference systems with an external field.
The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via B\"acklund transformation of the corresponding linear problems.
In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian)…
We review and compare different variational formulations for the Schr\"{o}dinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm…
For higher derivative theories, using the approach of Caratheodory's equivalent Lagrangian, we show that there exist novel formulations of Hamilton-Jacobi equations, which are different from the formulations derived from Hamilton's…
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…