Arbitrary high-order exponential integrators conservative schemes for the nonlinear Gross-Pitaevskii equation

In this paper, we propose a family of high-order conservative schemes based on the exponential integrators technique and the symplectic Runge-Kutta method for solving the nonlinear Gross-Pitaevskii equation. By introducing generalized scalar auxiliary variable, the equation is equivalent to a new system with both mass and modified energy conservation laws. Then, a conservative semi-discrete exponential scheme is given by combining the symplectic Runge-Kutta method and the Lawson method in the time direction. Subsequently, we apply the Fourier pseudo-spectral method to approximate semi-discrete system in space and obtain the fully -discrete schemes that conserve the energy and mass. Numerical examples are presented to confirm the accuracy and conservation of the developed schemes.

Automated summary

This paper proposes a family of high-order conservative schemes based on the exponential integrators technique and the symplectic Runge-Kutta method for solving the nonlinear Gross-Pitaevskii equation. Numerical examples are provided to confirm the accuracy and conservation of the developed schemes.