A variational approach to (m + 1)-dimensional n-order field

摘要

We present a method to construct the multisymplectic formulation for (m + 1)-dimensional n-order field based on the variational principle. Then we derive the multisymplectic conservation law and the local energy and momentum conservation laws for (m + 1)-dimensional n-order field. The centred box discretization of the multisymplectic formulation for (m + 1)-dimensional n-order field is proved to be a multisymplectic scheme. As an example, the process of constructing the multisymplectic formulation for the KP equation is given.