Related papers: Group invariant solutions and Conservation laws of…
Despite the large number of publications on symmetry analysis of the geopotential forecast equation, its group foliations laws have not been considered previously. The present publication aims to address this shortcoming. First, group…
A class of variable coefficient (1+1)-dimensional nonlinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u^nu_x)_x+h(x)u^m$ is investigated. Different kinds of equivalence groups are constructed including ones with…
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…
We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways.…
We perform the complete symmetry classification of the Klein-Gordon equation in maximal symmetric spacetimes. The central idea is to find all possible potential functions $V(t,x,y)$ that admit Lie and Noether symmetries. This is done by…
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…
In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how…
The application of the Gardner method for generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely B\"acklund transformations…
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…
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…
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…
In this paper we study the generalized variable-coefficient Gardner equations of the form $u_t + A(t)u^n\,u_x+ C(t)\,u^{2n}u_x + B(t)\,u_{xxx} + Q(t)\,u =0$. This class broadens out many other equations previously considered: Johnpillai and…
A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
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.
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…
We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic…
A systematic group-theoretical analysis of the supersymmetric sinh-Gordon equation is performed. A generalization of the method of prolongations is used to determine the Lie superalgebra of symmetries, and the method of symmetry reduction…
Given a class of differential equations with arbitrary element, the problems of symmetry group, nonclassical symmetry and conservation law classifications are to determine for each member the structure of its Lie symmetry group, conditional…
All possible linearly independent local conservation laws for $n$-dimensional diffusion--convection equations $u_t=(A(u))_{ii}+(B^i(u))_i$ were constructed using the direct method and the composite variational principle. Application of the…