Related papers: Self-adjointness and conservation laws of differen…
This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…
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…
Conservation laws are formulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples. The formulation does not…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the previous notions of self-adjoint and quasi self-adjoint…
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the…
In the present work, we formulate a generalization of the Noether Theorem for action-dependent Lagrangian functions. The Noether's theorem is one of the most important theorems for physics. It is well known that all conservation laws,…
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law…
This paper mainly contributes to the extension of Noether's theorem to differential-difference equations. For that purpose, we first investigate the prolongation formula for continuous symmetries, which makes a characteristic representation…
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to…
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…
We prove a fractional Noether's theorem for fractional Lagrangian systems invariant under a symmetry group both in the continuous and discrete cases. This provides an explicit conservation law (first integral) given by a closed formula…
The concept of nonlinear self-adjointness is employed to construct the conservation laws for fractional evolution equations using its Lie point symmetries. The approach is demonstrated on subdiffusion and diffusion-wave equations with the…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
Nonlinear self-adjointness method for constructing conservation laws of partial differential equations (PDEs) is further studied. We show that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…
In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…