相关论文: Quasi-Noether systems and quasi-Lagrangians
It is shown that the zilch conservation law arises as the Noether current corresponding to a variational symmetry of a duality-symmetric Maxwell Lagrangian. The action of the corresponding symmetry generator on the duality-symmetric…
Evidence and results suggesting that a Noether--like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics.…
We prove a Noether-type symmetry theorem for invariant optimal control problems with unrestricted controls. The result establishes weak conservation laws along all the minimizers of the problems, including those minimizers which do not…
The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general…
We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are…
In this paper we study symmetries, Newtonoid vector fields, conservation laws, Noether's Theorem and its converse, in the framework of the $k$-symplectic formalism, using the Fr\"olicher-Nijenhuis formalism on the space of $k^1$-velocities…
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…
In this work we prove a weak Noether type theorem for a class of variational problems which include broken extremals. We then use this result to prove discrete Noether type conservation laws for certain classes of finite element…
The Noether-like operators that play an essential role in writing down the invariants for systems of two ordinary differential equations (ODEs) are constructed. The classification of such operators is carried out with the help of analytic…
In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler--Lagrange equations,…
This paper provides a modern presentation of Noether's theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
Conservation laws are formulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples. The formulation does not…
This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…
Integrable velocity-dependent constraints are said to be semiholonomic. For good reasons, holonomic and semiholonomic constraints are thought to be indistinguishable in Lagrangian mechanics. This well-founded belief notwithstanding, here we…
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries are obtained and used to derive conservation laws via…
The investigation of approximate symmetries of reparametrization invariant Lagrangians of n + 1 degrees of freedom and quadratic velocities is presented. We show that extra conditions emerge which give rise to approximate and conditional…
This paper develops methods for simplifying systems of partial differential equations that have families of conservation laws which depend on functions of the independent or dependent variables. In some cases, such methods can be combined…
In this work, we propose a class of high order semi-Lagrangian scheme for a general consistent BGK model for inert gas mixtures. The proposed scheme not only fulfills indifferentiability principle, but also asymptotic preserving property,…
We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is a natural extension of the ideas known by the names "Lagrangian multiforms" and "Pluri-Lagrangian systems", which…