High-order structure-preserving algorithms for the multi-dimensional fractional nonlinear Schrödinger equation based on the SAV approach - Fu, Yayun; Hu, Dongdong; Wang, Yushun (Mathematics and computers in simulation, 2021)
In the paper, we aim to develop a class of high-order structure-preserving algorithms, which are built upon the idea of the newly introduced scalar auxiliary variable approach, for the multi-dimensional space fractional nonlinear Schrödinger equation. First, we reformulate the equation as an infinite-dimension canonical Hamiltonian system, and obtain an equivalent system with a modified energy conservation law by using the scalar auxiliary variable approach. Then, the new system is discretized by Gauss collocation methods to arrive at semi-discrete conservative systems. Subsequently, the Fourier pseudo-spectral method is applied for semi-discrete systems to obtain high-order fully-discrete schemes, which can both preserve the mass and the modified energy exactly in discrete scene. Finally, numerical experiments are provided to demonstrate the conservation and accuracy of the proposed schemes. •We derive the Hamiltonian formulation of the fractional nonlinear Schrödinger equation.•A class of high-order conservative schemes are devedloped for the equation.•Remarkable performances in the energy preservation and accuracy are obtained with the schemes.