Related papers: On conservation laws for the supersymmetric sigma …
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating…
We show that the so-called hidden potential symmetries considered in a recent paper [Gandarias M., Physica A, 2008, V.387, 2234-2242] are ordinary potential symmetries that can be obtained using the method introduced by Bluman and…
We use the general theory of local conservation laws for arbitrary partial differential equations to provide a geometric framework for conservation laws on characteristic null hypersurfaces. The operator of interest is the wave operator on…
The paper aims to study the connection between symmetries and conservation laws for the 2D Ricci flow model. The procedure starts by obtaining a set of multipliers which generates conservation laws. Then, using a general relation which…
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…
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…
For static reductions of isotropic and anisotropic Magnetohydrodynamics plasma equilibrium models, a complete classification of admitted point symmetries and conservation laws up to first order is presented. It is shown that the symmetry…
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…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
The properties of discrete nonlinear symmetries of integrable equations are investigated. These symmetries are shown to be canonical transformations. On the basis of the considered examples, it is concluded, that the densities of the…
In this paper, Lie symmetry method is performed for the Hirota-Ramani (H-R) equation. We will find The symmetry group and optimal systems of Lie subalgebras. Furthermore, preliminary classification of its group invariant solutions, symmetry…
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…
A global weak solution of the biharmonic wave map equation in the energy space for spherical targets is constructed. The equation is reformulated as a conservation law and solved by a suitable Ginzburg-Landau type approximation.
Motivated by BRST theory, we study generalized symmetries and supersymmetries depending on derivatives of dynamic variables in a most general setting. We state the first variational formula and conservation laws for higher order Lagrangian…
Noether's theorem on the equivalence of symmetry and conservation laws has applications to geometric problems on symmetric spaces. We remind the reader of the theorem and give an application to a variational problem on hyperbolic surfaces.
A fifth-order KdV equation with time dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations. For instance, they can be used to…
The methods of abstract simplicial homology and cohomology are reviewed and applied to the topology of electrical networks. Kirchhoffs laws of electrical circuits are shown to be manifestly homological in their origins. Since they are based…
I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such…
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation…