@article {Hydon1627,
author = {Hydon, P.E},
title = {Multisymplectic conservation laws for differential and differential-difference equations},
volume = {461},
number = {2058},
pages = {1627--1637},
year = {2005},
doi = {10.1098/rspa.2004.1444},
publisher = {The Royal Society},
abstract = {Many well-known partial differential equations can be written as multisymplectic systems. Such systems have a structural conservation law from which scalar conservation laws can be derived. These conservation laws arise as differential consequences of a 1-form {\textquoteleft}quasi-conservation law{\textquoteright}, which is related to Noether{\textquoteright}s theorem. This paper develops the above framework and uses it to introduce a multisymplectic structure for differential-difference equations. The shallow water equations and the Ablowitz{\textendash}Ladik equations are used to illustrate the general theory. It is found that conservation of potential vorticity is a differential consequence of two conservation laws; this surprising result and its implications are discussed.},
issn = {1364-5021},
URL = {http://rspa.royalsocietypublishing.org/content/461/2058/1627},
eprint = {http://rspa.royalsocietypublishing.org/content/461/2058/1627.full.pdf},
journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}
}