Multi-symplectic Fourier pseudospectral method for the Landau-Ginzburg-Higgs equation

In this paper, the multi-symplectic method is used to study an important nonlinear wave equation, named Landau-Ginzburg-Higgs equation. Firstly, the multi-symplectic form of the Landau-Ginzburg-Higgs equation is deduced using the Hamiltonian variational principle. Then, the explicit multi-symplectic discrete scheme is derived by applying the Fourier pseudospectral method to space derivatives and the symplectic Euler method to time derivatives in the multi-symplectic form. The soliton solution with non-periodic boundary is simulated by the proposed scheme. The numerical results show that: the proposed scheme can simulate the soliton solution well and can preserve the local conservation quantities.