Related papers: Symmetries, conservation laws and Noether's theore…
Noether's theorem provides a powerful link between continuous symmetries and conserved quantities for systems governed by some variational principle. Perhaps unfortunately, most dynamical systems of interest in neuroscience and artificial…
A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding classification of Hamiltonian symmetries…
The hierarchy of the integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of the linearization of these equations and their conservation law in the terms of the solutions of the…
In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed…
Algorithms for the symbolic computation of polynomial conservation laws, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations (DDEs) are presented. The algorithms can be used to test the…
We study a family of PDEs, which was derived as an approximation of an extended Lotka-Volterra system, from the point of view of symmetries. Also, by performing the self adjoint classification on that family we offer special cases…
Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretation of these symmetries as differential-difference equations…
We extend Noether's symmetry theorem to fractional action-like variational problems with higher-order derivatives.
A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field…
For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…
Noether's theorem is an elegant and powerful tool of classical mechanics, but it is of little to no consequence in discrete theories. Here we define and explore a discrete approach to covariant mechanics and show that within this framework…
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 conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
In this paper we study the infinitesimal symmetries, Newtonoid vector fields, infinitesimal Noether symmetries and conservation laws of Hamiltonian systems. Using the dynamical covariant derivative and Jacobi endomorphism on the cotangent…
Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conservation law. All conservation laws belong to the kernel of…
Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…
Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions of the linearization (Frechet derivative) equation holding on the space of solutions to the PDE, and they are well-known to…
We establish a new version of the first Noether Theorem, according to which the (equivalence classes of) first integrals of given Euler-Lagrange equations in one independent variable are in exact one-to-one correspondence with the…
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law…
We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both classical and quantum mechanics, observables…