## 2 Citations

### Symmetries, Conservation Laws, and Noether's Theorem for Differential‐Difference Equations

- Mathematics
- 2016

This paper mainly contributes to the extension of Noether's theorem to differential‐difference equations. For this purpose, we first investigate the prolongation formula for continuous symmetries,…

### A modified formal Lagrangian formulation for general differential equations

- MathematicsJapan Journal of Industrial and Applied Mathematics
- 2022

In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The…

## References

SHOWING 1-10 OF 32 REFERENCES

### Nonlinear self-adjointness and conservation laws

- Mathematics
- 2011

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…

### Characteristics of Conservation Laws for Difference Equations

- MathematicsFound. Comput. Math.
- 2013

The converse of Noether’s Theorem for difference equations is established, the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and all five-point conservation laws for the potential Lotka–Volterra equation are obtained.

### Relations between symmetries and conservation laws for difference systems

- Mathematics
- 2014

This paper presents a relation between divergence variational symmetries for difference variational problems on lattices and conservation laws for the associated Euler–Lagrange system provided by…

### Conservation laws of partial difference equations with two independent variables

- Mathematics
- 2001

This paper introduces a technique for obtaining the conservation laws of a given scalar partial difference equation with two independent variables. Unlike methods that are based on Nother's theorem,…

### Direct Construction of Conservation Laws from Field Equations

- Environmental Science
- 1997

This Letter presents an algorithm to obtain all local conservation laws for any system of field equations. The algorithm uses a formula which directly generates the conservation laws and does not…

### First integrals of ordinary difference equations beyond Lagrangian methods

- Mathematics
- 2013

A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation. The…

### Conservation laws for integrable difference equations

- Mathematics, Physics
- 2007

This paper deals with conservation laws for all integrable difference equations that belong to the famous Adler–Bobenko–Suris classification. All inequivalent three-point conservation laws are found,…

### Symmetries and first integrals of ordinary difference equations

- MathematicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2000

This paper describes a new symmetry-based approach to solving a given ordinary difference equation. By studying the local structure of the set of solutions, we derive a systematic method for…

### Symmetries and differential equations

- Mathematics
- 1981

The knowledge of the maximal Lie group or abstract monoid of symmetries of an ordinary non-singular differential equation (or system of equations) allows us to obtain solutions of them. Traditional…