Related papers: Conservation Laws for SO(p,q)
For nonlinear Schr\"odinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating…
Based on the gradient-holonomic algorithm we analyze the integrability property of the generalized hydrodynamical Riemann type equation $%D_{t}^{N}u=0$ for arbitrary $N\in \mathbb{Z}_{+}.$ The infinite hierarchies of polynomial and…
In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law satisfy a second order system of PDEs which has a natural…
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…
We propose a notion of hyperbolic system of conservation laws invariant for the Galileo group of transformations. We show that with natural physical and mathematical hypotheses, such a system conducts to the gas dynamics equations or to…
By the Cole-Hopf transformation, with any linear evolution equation in 1+1 dimensions a generalized Burgers equation is associated. We describe local conservation laws of these equations. It turns out that any generalized Burgers equation…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
The \nl \cls for the N=1 supersymmetric KdV equation are shown to be related in a simple way to powers of the fourth root of its Lax operator. This provides a direct link between the supersymmetry invariance and the existence of \nl…
Nonlinear self-adjointness method for constructing conservation laws of partial differential equations (PDEs) is further studied. We show that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation…
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…
This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87…
We derive conservation laws for energy-momentum (canonical and dynamical) and angular momentum for a general Lorentz connection.
Basic features of the conservation laws in the Hamiltonian approach to the Poincar\'e gauge theory are presented. It is shown that the Hamiltonian is given as a linear combination of ten first class constraints. The Poisson bracket algebra…
We consider branching laws for the restriction of some irreducible unitary representations $\Pi$ of $G=O(p,q)$ to its subgroup $H=O(p-1,q)$. In Kobayashi (arXiv:1907.07994), the irreducible subrepresentations of $O(p-1,q)$ in the…
Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov, we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and…
For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for…
Systems of nonlinear ordinary differential equations are constructed, for which the general solution is algebraically expressed in terms of a finite number of particular solutions. Expressions of that type are called the nonlinear…
The nonlinear partial differential equations describing the spin dynamics of Heisenberg ferro and antiferromagnet are studied by Lie transformation group method. The generators of the admitted variational Lie symmetry groups are derived and…