一类广义不稳定时空分数阶薛定谔方程的近似解  

Approximate solutions to a class of generalized time-space fractional unstable Schr dinger equation

作　　者：洪宝剑[1] HONG Baojian(Faculty of Mathematical Physics,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院数理学院,江苏南京211167

出　　处：《安徽大学学报（自然科学版）》2023年第1期17-23,共7页Journal of Anhui University(Natural Science Edition)

基　　金：江苏省高等学校自然科学研究基金资助项目(18KJB110013);江苏省大学生实践创新训练计划指导项目(202211276054Y)。

摘　　要：基于求分数阶非线性偏微分方程近似解的迭代思想,通过将Laplace变换与同伦摄动法相结合,借助Adomian多项式展开和对非线性项进行修正,构造出合乎模型的近似解标准迭代式.研究一类广义不稳定时空分数阶薛定谔方程,得到该方程的各级近似解表达式,这些解在极限情形下可转化为精确解,通过误差分析及数值模拟将两者进行比较,发现其实部、虚部与模之间接近程度良好,结果表明该近似算法在求解常系数及变系数时空分数阶非线性薛定谔方程时规范有效.Based on the iterative idea of finding the approximate solutions of fractional nonlinear partial differential equations,by combining Laplace transform with homotopy perturbation method,and by means of Adomian polynomials expansion and correction of nonlinear terms,the standard iterative formula of approximate solutions conforming to the related model was constructed.A class of generalized unstable time-space fractional Schr dinger equations was studied,and the expressions of various approximate solutions of the equations were obtained.These solutions could be converted into exact solutions in the limit case.Through error analysis and numerical simulation,it was found that the real part,imaginary part and module were close to each other.The results showed that the approximation algorithm was effective in solving the time-space fractional nonlinear Schr dinger equation with constant or variable coefficients.

关 键 词：时空分数阶薛定谔方程 LAPLACE变换 ADOMIAN多项式 CAPUTO导数 近似解 

分 类 号：O175.2[理学—数学]