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
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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…