Multi-symplectic scheme for the coupled Schrödinger–Boussinesq equations

In this paper, a multi-symplectic Hamiltonian formulation is presented for the coupled Schrödinger–Boussinesq equations (CSBE). Then, a multi-symplectic scheme of the CSBE is derived. The discrete conservation laws of the Langmuir plasmon number and total perturbed number density are also proved. Numerical experiments show that the multi-symplectic scheme simulates the solitary waves for a long time, and preserves the conservation laws well.