相关论文: Conservation Laws and Hamilton's Equations for Sys…

In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we…

In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence…

Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space-time scale. In these…

Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…

The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…

In this paper, we derive the time-fractional Cahn-Hilliard equation from continuum mixture theory with a modification of Fick's law of diffusion. This model describes the process of phase separation with nonlocal memory effects. We analyze…

The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second order perturbative approach. The resulting expression allows for the analysis of some…

A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…

We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians…

By dispersive models of fluid mechanics we are referring to the Euler-Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is…

Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the…

We show that the equation of quasigeostrophic (QG) potential vorticity conservation in geophysical fluid dynamics follows from Hamilton's principle for stationary variations of an action for geodesic motion in the f-plane case or its…

It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…

The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains…

We study conservation laws of a general class of quantum many-body systems subjected to an external time dependent quasi-periodic driving. {When the frequency of the driving is large enough or the strength of the driving is small enough, we…

The momentum conservation law for general dissipationless reduced-fluid (e.g., gyrofluid) models is derived by Noether method from a variational principle. The reduced-fluid momentum density and the reduced-fluid canonical momentum-stress…

In this paper we consider the relation between symmetries and first integrals for both continuous canonical Hamiltonian equations and discrete Hamiltonian equations. We observe that canonical Hamiltonian equations can be obtained by…

In contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether's theorem for non-autonomous contact Hamiltonian systems,…

Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but…