Multisymplectic Geometry and Multisymplectic Scheme for the Nonlinear Klein Gordon Equation

Abstract

The multisymplectic structure of the Nonlinear Klein Gordon equation is presented directly from the variational principle. In the numerical aspect, we give a multisymplectic nine points scheme which is equivalent to the multisymplectic Preissmann scheme. A series of numerical results are reported to show the effectiveness of the scheme.