Higher order symmetry operators for the wave equation with scalar and vector potentials are investigated. All scalar potentials which admit second order symmetry operators are found explicitly. Symmetries of partial differential equations are used for separation of variables [1], description of conservation laws [2], construction of exact solutions [3], etc. Before can be applied, symmetries ha...

The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...

We consider a four dimensional space-time symmetry which is a non trivial extension of the Poincaré algebra, different from supersymmetry and not contradicting a priori the well-known no-go theorems. We investigate some field theoretical aspects of this new symmetry and construct invariant actions for non-interacting fermion and noninteracting boson multiplets. In the case of the bosonic multip...

On the basis of recent results extending non-trivially the Poincaré symmetry, we investigate the properties of bosonic multiplets including 2−form gauge fields. Invariant free Lagrangians are explicitly built which involve possibly 3− and 4−form fields. We also study in detail the interplay between this symmetry and a U(1) gauge symmetry, and in particular the implications of the automatic gaug...

This paper is concerned with a class of ten time-fractional polynomial evolution equations. The one-parameter Lie point symmetries these equations are found and the symmetry reductions provided. These reduced transformed into nonlinear ordinary differential equations, which challenging to solve by conventional methods. We search for power series solutions demonstrate convergence properties such...

Title of Dissertation: Control and Stabilization of a Class of Nonlinear Systems with Symmetry Vikram Manikonda, Doctor of Philosophy, 1998 Dissertation directed by: Professor P.S. Krishnaprasad Department of Electrical Engineering The focus of this dissertation is to study issues related to controllability and stabilization of a class of underactuated mechanical systems with symmetry. In parti...

We introduce a general framework for the construction of variational integrators of arbitrarily high-order that incorporate Lie group techniques to automatically remain on a Lie group, while retaining the geometric structure-preserving properties characteristic of variational integrators, including symplecticity, momentum-preservation, and good long-time energy behavior. This is achieved by con...

Symmetries play important roles in mathematics, physics and mechanics. Since Noether unveiled the profound relations between symmetries and conservation laws, many researches on them were done [1–15]. Recently, symmetry theories have been extended to discrete mechanics and equations [16–25]. As we know, even tiny changes in symmetry, named as perturbation to symmetry, are of great importance fo...

Axioms of Lie algebroid are discussed. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the C∞(M)-module E of sections of a vector bundle E over a manifold M which satisfies [X, fY ] = f [X, Y ] + A(X,f)Y for all X, Y ∈ E , f ∈ C∞(M), and for certain A(X,f) ∈ C∞(M)) is a Lie algebroid if rank(E) > 1, and is a local Lie algebra in the sense of Kirillov if E is a ...

Singular system has great relationship with gauge field theory, condensed matter theory and some other research areas. Based on the mixed integer Riemann-Liouville fractional derivatives, singular is studied. Firstly, constrained Hamilton equation inherent constraint are presented. Secondly, Lie symmetry conserved quantity analyzed, including determined equation, limited additional structural e...