A canonical multisymplectic formulation of the KdV equation is presented which, when space + time decomposed, gives rise to the usual symplectic description of dynamics on the appropriate space of Cauchy data. In adddition to allowing one to treat the KdV equation covariantly, this formalism enables one to derive the Gardner symplectic structure for the KdV equation in a completely systematic way.
11 pps.
1987
Published in: Differential Geometric Methods in Theoretical Physics, K. Bleuler & M. Werner, Eds., NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences, 250, 295--305 (Kluwer, Dordrecht, 1988).