A LINEARLY-IMPLICIT ENERGY-PRESERVING ALGORITHM FOR THE TWO-DIMENSIONAL SPACE-FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION BASED ON THE SAV APPROACH  

作　　者：Yayun Fu Wenjun Cai Yushun Wang 

机构地区：[1]School of Science,Xuchang University,Xuchang 461000,China [2]Jiangsu Key Laboratory for NSLSCS,Jiangsu Collaborative Innovation Center of Biomedial Functional Materials,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China

出　　处：《Journal of Computational Mathematics》2023年第5期797-816,共20页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12171245,11971416,11971242);the Natural Science Foundation of Henan Province(No.222300420280);the Program for Scientific and Technological Innovation Talents in Universities of Henan Province(No.22HASTIT018).

摘　　要：The main objective of this paper is to present an efficient structure-preserving scheme,which is based on the idea of the scalar auxiliary variable approach,for solving the twodimensional space-fractional nonlinear Schrodinger equation.First,we reformulate the equation as an canonical Hamiltonian system,and obtain a new equivalent system via introducing a scalar variable.Then,we construct a semi-discrete energy-preserving scheme by using the Fourier pseudo-spectral method to discretize the equivalent system in space direction.After that,applying the Crank-Nicolson method on the temporal direction gives a linearly-implicit scheme in the fully-discrete version.As expected,the proposed scheme can preserve the energy exactly and more efficient in the sense that only decoupled equations with constant coefficients need to be solved at each time step.Finally,numerical experiments are provided to demonstrate the efficiency and conservation of the scheme.

关 键 词：Fractional nonlinear Schrodinger equation Hamiltonian system Scalar auxiliary variable approach Structure-preserving algorithm 

分 类 号：O175[理学—数学]