TY - JOUR
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
SP - 1627
LP - 1637
M3 - 10.1098/rspa.2004.1444
VL - 461
IS - 2058
AU - Hydon, P.E
Y1 - 2005/06/08
UR - http://rspa.royalsocietypublishing.org/content/461/2058/1627.abstract
N2 - 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.
ER -