2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57302In this paper we discussed the self-adjointness of the Maxwell's equations with variable coefficients $ε$ and $μ$. Three different Lagrangian are attained. By the Legendre transformation, a multisymplectic Bridge's (Hamilton) form is obtained. Based on the multisymplectic structure, the multisymplectic conservation law of the system is derived and a nine-point Preissman multisymplectic scheme which preserve the multisymplectic conservation law is given for the Maxwell's equations in an inhomogeneous, isotropic and lossless medium. At last a numerical example is illustrated.13 pages, 4 figuresMathematical Physicstext