相关论文: A Discourse on the Benney Equation
The generalized transport equations for a consistent description of kinetic and hydrodynamic processes in dense gases and liquids are considered. The inner structure of the generalized transport kernels for these equations is established.…
It is feasible to obtain any basic rule of the already known Quantum Mechanics applying the Hamilton-Jacobi formalism to an interacting system of 2 fermionic degrees of freedom. The interaction between those fermionic variables unveils also…
The paper is devoted to prove the existence of a local solution of the Hamilton-Jacobi equation in field theory, whence the general solution of the field equations can be obtained. The solution is adapted to the choice of the submanifold…
We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including the acceleration term) where the force is created by the interactions with the other particles and with a periodic…
A calculation of the classical analogue for the quantum wave function and local denity of states, in energy representation, is presented for simple Hamiltonian systems. Sucha analogous were proposed by M. V. Berry and A. voros considering…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
The tree formula, which relates proper and connected vertices, is shown to be the solution to a Hamilton-Jacobi equation.
The mechanism of irreversible dynamics in the mixing systems is constructed in the frames of the classical mechanics laws. The offered mechanism can be found only within the framework of the generalized Hamilton's formalism. The generalized…
The decomposition of the energy of a compressible fluid parcel into slow (deterministic) and fast (stochastic) components is interpreted as a stochastic Hamiltonian interacting particle system (HIPS). It is shown that the McKean-Vlasov…
The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given…
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
We prove the existence of $C^{1}$ critical subsolutions of the Hamilton-Jacobi equation for a time-periodic Hamiltonian system. We draw a consequence for the Minimal Action functional of the system.
The paper studies a system of first order Hamilton-Jacobi equations with discontinuous coefficients, arising from a model of deterministic optimal debt management in infinite time horizon, with exponential discount and currency devaluation.…
A new direct integration method is established to construct the solutions of the stationary BBGKY hierarchy, assuming the usual form of the equilibrium correlation functions, for infinite classical systems of particles interacting via a…
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
We discuss an extension of the Hamilton-Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the…