2015•SymmetryOpen access

Conservation Laws of Discrete Evolution Equations by Symmetries and Adjoint Symmetries

Wen‐Xiu Ma

Abstract

A direct approach is proposed for constructing conservation laws of discrete evolution equations, regardless of the existence of a Lagrangian. The approach utilizes pairs of symmetries and adjoint symmetries, in which adjoint symmetries make up for the disadvantage of non-Lagrangian structures in presenting a correspondence between symmetries and conservation laws. Applications are made for the construction of conservation laws of the Volterra lattice equation.

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Key concepts: Conservation law, Homogeneous space, Lagrangian, Mathematics, Lattice (music), Adjoint equation, Mathematical physics, Applied mathematics