Related papers: Group classification of variable coefficient gener…
It is shown for a simple ODE that it has many symmetry groups beyond its usual Lie group symmetries, when its generalized solutions are considered within the nowhere dense differential algebra of generalized functions.
In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and…
Starting with a finite-dimensional complex Lie algebra, we extend scalars using suitable commutative topological algebras. We study Birkhoff decompositions for the corresponding loop groups. Some results remain valid for loop groups with…
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…
The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in papers on this method are discussed and strategies to overcome…
We study the Lie point symmetries of semilinear Kohn-Laplace equations on the Heisenberg group H^1 and obtain a complete group classification of these equations.
We obtain complete classification of in-equivalent realizations of the Virasoro algebra by Lie vector fields over the three-dimensional field of real numbers. As an application we construct new classes of nonlinear second-order partial…
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in…
The generalized Kuramoto-Sivashinsky equation in the case of the power nonlinearity with arbitrary degree is considered. New exact solutions of this equation are presented.
This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…
We discuss a generalization of Clifford algebras known as generalized Clifford algebras (in particular, ternary Clifford algebras). In these objects, we have a fixed higher-degree form (in particular, a ternary form) instead of a quadratic…
We consider a class of (1+2)-dimensional linear partial differential of Asian options pricing. Special cases have been used to models of financial mathematics. We carry out group classification of a class equations. In particular, the…
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
By using the Lie's invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schr\"{o}dinger equations with variable coefficients. Starting from the equivalence generators we construct…
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
Let $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer…
There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the…
The cohomology groups of Lie superalgebras and, more generally, of color Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is non-trivial. Two general propositions are proved,…
symmetry, group classification, differential invariants, Lie-classical method,infinitesimal criterion method, RDC equation, KPP equation, similarity solutions.