Abstract
The FORQ equation, which is bi-Hamiltonian, integrable, and hosts of a range of soliton solutions, is viewed afresh from the viewpoint of multi-symplectic structures. A multi-symplectic formulation is derived and used as a guide in the construction of numerical methods for simulation; in particular, a multi-symplectic Preissmann box scheme is constructed for the FORQ equation, which is second-order accurate in both space and time. Simulations show that the cuspons and the W/M-shape-peaks solitons for the FORQ equation are reproduced accurately. To verify the precision and the validity of the numerical results, the relative errors between the numerical results and the theoretical solutions, and the maximum values of the errors of the local conservation laws are presented.