Related papers: Hamilton-Jacobi theory for one dimensional autonom…
We investigate a singular perturbation for Hamilton-Jacobi equations in an open subset of two dimensional Euclidean space, where the set is determined through a Hamiltonian function and the Hamilton-Jacobi equations are the dynamic…
In this paper, we revisit the technique of doubling variables in first order Hamilton-Jacobi equations, especially when the equations arise in optimal control. We show that by tuning the penalization between the two points, we can change…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the…
We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the…
The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate…
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…
The Hamilton-Jacobi method is generalized, both, in classical and relativistic mechanics. The implications in quantum mechanics are considered in the case of Klein-Gordon equation. We find that the wave functions of Klein-Gordon theory can…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the…
Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of quasi periodic…
In this paper we use the theory of viscosity solutions for Hamilton-Jacobi equations to study propagation phenomena in kinetic equations. We perform the hydrodynamic limit of some kinetic models thanks to an adapted WKB ansatz. Our models…
The paper deals with Hawking radiation related to non-static spherically symmetric black hole. Quantum corrections are incorporated using Hamilton-Jacobi method beyond semi-classical approximation. It is found that different order…
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some…
We develop a Hamilton-Jacobi theory for singular lagrangian systems using the Gotay-Nester-Hinds constraint algorithm. The procedure works even if the system has secondary constraints.
In this article, the quantum Hamilton- Jacobi theory based on the position dependent mass model is studied. Two effective mass functions having different singularity structures are used to examine the Morse and Poschl- Teller potentials.…
This paper presents a novel Hamiltonian formulation of the isotropic Navier-Stokes problem based on a minimum-action principle derived from the principle of least squares. This formulation uses the velocities $u_{i}(x_{j},t)$ and pressure…
A Hamilton-Jacobi formalism for thermodynamics was formulated by Rajeev [Ann. Phys. 323, 2265 (2008)] based on the contact structure of the odd dimensional thermodynamic phase space. This allows one to derive the equations of state of a…
Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear…