Energy Preserving Parametric Multi-symplectic Methods for the Gross-Pitaevskii Equation

Abstract The multi-symplectic structure and energy conservation are inherent properties of the Gross-Pitaevskii equation. In this paper, we propose classical multi-symplectic Runge-Kutta methods and parametric multi-symplectic Runge-Kutta methods for the one-dimensional Gross-Pitaevskii equation. The parametric methods not only inherit the multi-symplectic structure and quadratic invariants of the classical methods, but also achieve energy conservation in a weaker sense by introducing an additional parameter. Numerical experiments verify the effectiveness of the proposed methods. Mathematics Subject Classification (2020) 65M06 · 65M12 · 65Z05 · 70H15