Related papers: The Differential and Functional Equations for a Li…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…
In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations with functional derivatives. In order to perform the group analysis and deal with the functional…
Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which…
In this paper, a method to solve functionally commutative time- dependent linear homogeneous differential equation is discussed. We apply this technique to solve some dynamical quantum problems.
We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an…
We show that there is an one-to-one correspondence between resolutions (equivariant w.r.t. a Lie groupoid action) of a singular subset of a manifold, and substacks (of a certain type) of the differential stack associated to the Lie groupoid…
An isomorphism between two hermitian unitals is proved, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).
In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.
It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…
We discuss a Moser type argument to show when a deformation of a Lie group homomorphism and of a Lie subgroup is trivial. For compact groups we obtain stability results.
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to…
We solve the differentiation problem for Lie $\infty$-groups. Our approach builds on a classical version of Cartier duality which canonically identifies the Hopf algebra of point distributions supported at the identity of a Lie group with…
Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.
Over a large class of function fields, we show that the solutions of some linear equations in the topological closure of a certain subgroup of the group of units in the function field are exactly the solutions that are already in the…
Our aim in this paper is to prove, under some growth conditions on the datas, the solvability in a Gevrey class of a polynomially nonlinear functional differential equation.