相关论文: The Invariance and Conservation Laws of fourth-ord…
We obtain the optimal system's generating operators associated with the kind generalization of the Levinson Smith equation. Using those operators we characterize all invariant solutions associated with this equation. Moreover, we present…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
A fifth-order KdV equation with time dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations. For instance, they can be used to…
We apply the theory of Lie symmetries in order to study a fourth-order $1+2$ evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries…
The explicit formulation of the general inverse problem on conservation laws is presented for the first time. In this problem one aims to derive the general form of systems of differential equations that admit a prescribed set of…
Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and…
While not generally a conservation law, any symmetry of the equations of motion implies a useful reduction of any second-order equationto a first-order equation between invariants, whose solutions (first integrals) can then be integrated by…
The paper compares computational aspects of four approaches to compute conservation laws of single differential equations (DEs) or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer…
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…
The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of the equations, and symmetries and conservation laws in Eulerian coordinates are…
We study the nonlinear wave equation for arbitrary function with fourth order dissipation. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth…
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…
Invariant finite-difference schemes for the one-dimensional shallow water equations in the presence of a magnetic field for various bottom topographies are constructed. Based on the results of the group classification recently carried out…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
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…
We consider the calculation of Euler--Lagrange systems of ordinary difference equations, including the difference Noether's Theorem, in the light of the recently-developed calculus of difference invariants and discrete moving frames. We…
In this paper, we highlight the complimentary nature of the results of Anco & Bluman and Ibragimov in the construction of conservation laws; that whilst the former establishes the role of multipliers, the latter presents a formal procedure…
A Lagrangian formalism for variational second-order delay ordinary differential equations (DODEs) is developed. The Noether operator identity for a DODE is established, which relates the invariance of a Lagrangian function with the…
Within the framework of inverse Lie problem, we give some non-trivial examples of coupled Lie remarkable equations, \textit{i.e.}, classes of differential equations that are in correspondence with their Lie point symmetries. In particular,…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…