Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation

The multisymplectic structure of the KdV equation is presented directly from the variational principle. From the numerical view point, we give a multisymplectic twelve-points scheme which is equivalent to the multisymplectic Preissmann scheme. Finally, we test the twelve-points scheme on solitary waves over long time intervals.

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