A Derivation of Conserved Quantities and Symmetries for the Multi-Dimensional Soliton Equations
Since the study on the KdV equation by Miura[l], it has been shown that soliton equations have the remarkable properties, the existence of an infinite number of conserved quantities and symmetries. Several methods have been proposed successfully to show these properties for the equations which have one spatial dimension. However, for the higher dimensional cases or for the discrete equations, the problems are rather complicated and it is not so easy to give the explicit expressions.
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