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arXiv · 1405.4947

Self-adjointness and conservation laws of difference equations

Linyu Peng
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Abstract

A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.

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Linyu Peng. 2014-05-20. Self-adjointness and conservation laws of difference equations. https://doi.org/10.1016/j.cnsns.2014.11.003

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