ON HAMILTONIAN FORMULATIONS AND CONSERVATION LAWS FOR PLATE THEORIES OF VEKUA-AMOSOV TYPE

Conservation laws of semidiscrete canonical Hamiltonian equations

There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one–parameter Hamiltonian symmetries admitted by the PDEs [1]. The same result holds for semidiscrete Hamiltonian equations [2]. In this paper we consider semidiscrete canonical Hamiltonian equations. Using symmetries, we find conservation laws for...

On Hamiltonian perturbations of hyperbolic systems of conservation laws

We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially one-dimensional systems of hyperbolic PDEs vt + [φ(v)]x = 0. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on t...

Stability and Geometric Conservation Laws for Ale Formulations

Lagrangian and Hamiltonian formulations of higher order Chern-Simons theories

We consider models involving the higher (third) derivative extension of the abelian Chern-Simons (CS) topological term in D=2+1 dimensions. The polarisation vectors in these models reveal an identical structure with the corresponding expressions for usual models which contain, at most, quadratic structures. We also investigate the Hamiltonian structure of these models and show how Wigner’s litt...

Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...