Numerical simulation of interaction between Schrödinger field and Klein–Gordon field by multisymplectic method

We propose a multisymplectic scheme to solve the coupled Klein–Gordon–Schrödinger system. The scheme preserves the multisymplectic geometry structure exactly by satisfying the discrete multisymplectic conservation law, and can simulate the original waves well in a long time. This scheme also has discrete quasi-norm conservation law. Numerical experiments demonstrate the consistency between the theoretical analysis and the numerical results.