Structure-preserving analysis of perturbed Landau-Ginzburg-Higgs equation

Aim. Perturbation effect, one of the important essential attributes of practical physical and mechanical systems, should be reappeared in the structure-preserving analysis process. We now propose the generalized multi-symplectic method to study the perturbation effect of the perturbed Landau-Ginzburg-Higgs equation based on the developing theory of multi-symplecticity. Sections 1 through 3 of the full paper explain our explorative research in some detail. The core of section 1 is that we derive eq. (4) as the generalized multi-symplectic form for the perturbed Landau-Ginzburg-Higgs equation. The core of section 2 is that we construct the structure-preserving difference scheme eq. (5) for the generalized multi-symplectic form eq. (4). The core of section 3 is that we analyze the perturbation effect of the perturbed Landau-Ginzburg-Higgs equation system with the generalized multi-symplectic method. The results of this paper and their analysis appear to allow studying in a new way the nonconservative type geometric properties of the Hamilton system.