Novel High-Order Mass-and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrodinger Equation  

作　　者：Xu Qian Hong Zhang Jingye Yan Songhe Song 

机构地区：[1]Department of Mathematics,National University of Defense Technology,Changsha 410073,China [2]College of Mathematics and Physics,Wenzhou University,Wenzhou 325000,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第4期993-1012,共20页高等学校计算数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(12271523,11901577,11971481,12071481);the National Key R&D Program of China(SQ2020YFA0709803);the Defense Science Foundation of China(2021-JCJQ-JJ-0538);the National Key Project(GJXM92579);the Natural Science Foundation of Hunan(2020JJ5652,2021JJ20053);the Research Fund of National University of Defense Technology(ZK19-37,ZZKY-JJ-21-01);the Science and Technology Innovation Program of Hunan Province(2021RC3082);the Research Fund of College of Science,National University of Defense Technology(2023-lxy-fhjj-002).

摘　　要：We develop a class of conservative integrators for the regularized logarithmic Schrodinger equation(RLogSE)using the quadratization technique and symplectic Runge-Kutta schemes.To preserve the highly nonlinear energy functional,the regularized equation is first transformed into an equivalent system that admits two quadratic invariants by adopting the invariant energy quadratization approach.The reformulation is then discretized using the Fourier pseudo-spectral method in the space direction,and integrated in the time direction by a class of diagonally implicit Runge-Kutta schemes that conserve both quadratic invariants to round-off errors.For comparison purposes,a class of multi-symplectic integrators are developed for RLogSE to conserve the multi-symplectic conservation law and global mass conservation law in the discrete level.Numerical experiments illustrate the convergence,efficiency,and conservative properties of the proposed methods.

关 键 词：Regularized logarithmic Schrödinger equation conservative numerical integrators invariant energy quadratization approach diagonally implicit Runge-Kutta scheme 

分 类 号：O17[理学—数学]