RT Journal Article
SR Electronic
T1 Multisymplectic conservation laws for differential and differential-difference equations
JF Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
JO PROC R SOC A
FD The Royal Society
SP 1627
OP 1637
DO 10.1098/rspa.2004.1444
VO 461
IS 2058
A1 Hydon, P.E
YR 2005
UL http://rspa.royalsocietypublishing.org/content/461/2058/1627.abstract
AB 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 ‘quasi-conservation law’, which is related to Noether'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–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.