非线性耦合薛定谔方程组的保能量DFF格式
Energy-Preserving DFF Scheme for the Coupled Nonlinear Schr?dinger Equations
DOI: 10.12677/PM.2022.1210187, PDF,  被引量    国家自然科学基金支持
作者: 王启红, 杨 姗：南昌航空大学，数学与信息科学学院，江西 南昌
关键词: 非线性耦合薛定谔方程组；保结构性；Du Fort-Frankel格式；Coupled Nonlinear Schr?dinger Equations； Mass and Energy Conservation； Du Fort-Frankel Scheme
摘要: 对于具有保结构的非线性耦合薛定谔方程组，多为隐式求解且需要迭代求解，则需要花费昂贵的CPU时间。即本文为了克服非线性耦合薛定谔方程组(CNLS)计算效率低的问题，提出了高效率的Du Fort-Frankel (DFF)格式，理论证明了格式的保结构性。最后数值结果验证了格式的有效性和保结构性，同时在空间网格h，时间步长 的情况下，得到数值解在空间方向和时间方向上具有二阶的收敛精度。并数值模拟了孤子间的碰撞，得出矢量孤子不仅可以相互反弹也可以相互束缚。
Abstract: For the nonlinear coupled Schrödinger equations with structure-preserving, most of them are solved implicitly and need to be solved iteratively, which requires expensive CPU time. That is, in order to overcome the problem of low computational efficiency of nonlinear coupled Schrödinger equations (CNLS), this paper proposes a highly efficient Du Fort-Frankel (DFF) scheme, which theoretically proves that the scheme is structure-preserving. Finally, numerical results verify the validity and structure preservation of the scheme. At the same time, under the condition of space grid h and time step , the numerical solution has second-order convergence accuracy in space and time directions. The collision between solitons is numerically simulated, and it is concluded that vector solitons can not only bounce off each other but also bind each other.
文章引用：王启红, 杨姗. 非线性耦合薛定谔方程组的保能量DFF格式[J]. 理论数学, 2022, 12(10): 1720-1735. https://doi.org/10.12677/PM.2022.1210187

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