A Compact Scheme for Coupled Stochastic Nonlinear Schrodinger Equations  

作　　者：Chuchu Chen Jialin Hong Lihai Ji Linghua Kong 

机构地区：[1]Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]Institute of Applied Physics and ComputationalMathematics,Beijing 100094,China [3]School of Mathematics and Information Science,Jiangxi Normal University,Nanchang,Jiangxi 330022,China

出　　处：《Communications in Computational Physics》2017年第1期93-125,共33页计算物理通讯（英文）

基　　金：This work was supported by the National Natural Science Foundation of China(Nos.91530118,91130003,11021101,11290142,11471310,11601032,11301234,11271171);the Provincial Natural Science Foundation of Jiangxi(Nos.20142BCB23009,20161ACB20006,20151BAB201012).

摘　　要：In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger equations.We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law,discrete charge conservation law and discrete energy evolution law almost surely.Numerical experiments confirm well the theoretical analysis results.Furthermore,we present a detailed numerical investigation of the optical phenomena based on the compact scheme.By numerical experiments for various amplitudes of noise,we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time.In particular,if the noise is relatively strong,the soliton will be totally destroyed.Meanwhile,we observe that the phase shift is sensibly modified by the noise.Moreover,the numerical results present inelastic interaction which is different from the deterministic case.

关 键 词：Coupled stochastic nonlinear Schrodinger equations compact scheme stochastic multi-symplectic conservation law energy evolution law charge conservation law soliton evolution soliton interaction 

分 类 号：O17[理学—数学]