相关论文: Lie Algebra Classification, Conservation Laws and …

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…

Lie symmetry group method is applied to study for the higher order Camassa-Holm equation. The symmetry group and its optimal system are given. Furthermore, preliminary classification of its group invariant solutions, symmetry reduction and…

In the present paper, a class of partial differential equations related to various plate and rod problems is studied by Lie transformation group methods. A system of equations determining the generators of the admitted point Lie groups…

English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…

We determine the Lie point symmetries of a Gardner type system and establish its nonlinear self-adjointness. We then construct conservation laws via Ibragimov's Theorem.

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential…

The Lie symmetry method is applied to derive the point symmetries for the N-dimensional fractional heat equation. We find that that the numbers of symmetries and Lie brackets are reduced significantly as compared to the nonfractional order…

Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are…

We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…

Using the basic prolongation method and the infinitesimal criterion of invariance, we find the most general Lie point symmetries group of the Thomas equation. Looking the adjoint representation of the obtained symmetry group on its Lie…

Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated…

In this paper, Lie symmetry method is performed for the Hirota-Ramani (H-R) equation. We will find The symmetry group and optimal systems of Lie subalgebras. Furthermore, preliminary classification of its group invariant solutions, symmetry…

We establish a version of the first Noether Theorem, according to which the (equivalence classes of) conserved quantities of given Euler-Lagrange equations in several independent variables are in one-to-one correspondence with the…

In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we…

A new method for the Lie group classification of differential equations is proposed. It is based of the determination of all possible cases of linear dependence of certain indeterminate appearing in the determining equations of symmetries…

We consider difference equations of order four and determine the one parameter Lie group of transformations (Lie symmetries) that leave them invariant. We introduce a technique for finding their first integrals and discuss the association…

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…

The degenerate coupled multi-KdV equations for coupled multiplicity l=3 are studied. The equations also known as three fields Kaup-Boussinesq equations are considered for invariant analysis and conservation laws. The classical Lie's…

We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with $n$ independent and $m$ dependent variables ($n\times m$ systems). We solve the symmetry conditions in a geometric way and…

Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…