Related papers: Connections Between Symmetries and Conservation La…
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 embark on a systematic study of continuous non-invertible symmetries, focusing on 1+1d CFTs. We describe a generalized version of Noether's theorem, where continuous non-invertible symmetries are associated to $\textit{non-local}$…
In this paper, we mainly study the integrability of 1+1 dimensional dispersive long-wave equation. Firstly, the Lie symmetry analysis of the equation is carried out in the first part. And the optimal system of the equation is obtained…
A theorem due to Nail H. Ibragimov (2007) provides a connection between symmetries and conservation laws for arbitrary differential equations. The theorem is valid for any system of differential equations provided that the number of…
In the past few years both non-Noether symmetries and bidifferential calculi has been successfully used in generating conservation laws and both lead to the similar families of conserved quantities.Here relationship between Lutzky's…
Symmetries of the one-dimensional shallow water magnetohydrodynamics equations (SMHD) in Gilman's approximation are studied. The SMHD equations are considered in case of a plane and uneven bottom topography in Lagrangian and Eulerian…
In this paper, the nonlinear Rosenau-Hyman equation with time dependent variable coefficients is considered for investigating its invariant properties, exact solutions and conservation laws. Using Lie classical method, we derive symmetries…
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are…
In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the corresponding dissipated quantities. We notice that in…
In this paper we consider generalization of procedure of construction of potential systems for systems of partial differential equations with multidimensional spaces of conservation laws. More precisely, for construction of potential…
We introduce a sub-symmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire system. We discuss the geometrical meaning and properties…
For nonlinear Schroedinger equations with a power nonlinearity, a new approach to derive the conservation law of the momentum and the pseudo conformal conservation law is obtained. Since this approach does not contain approximating…
Noether's theorem is widely regarded as one of the most elegant results in theoretical physics. The article presents two simple examples that can be used to demonstrate the basic idea behind Noether's theorem, by deriving a relation between…
Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
We describe a methodology to build vectorial kinetic schemes, targetting the numerical solution of linear symmetric-hyperbolic systems of conservation laws -a minimal application case for those schemes. Precisely, we fully detail the…
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabelling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A…
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical…
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,…
This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…
A new approach, combining the Ibragimov method and the one by Anco and Bluman, with the aim of algorithmically computing local conservation laws of partial differential equations, is discussed. Some examples of the application of the…