ON FOURIER TIME-SPLITTING METHODS FOR NONLINEAR SCHR?DINGER EQUATIONS IN THE SEMICLASSICAL LIMIT~?

RéMI CARLES

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ON FOURIER TIME-SPLITTING METHODS FOR NONLINEAR SCHR?DINGER EQUATIONS IN THE SEMICLASSICAL LIMIT~?

机译：半经典极限下非线性Schrüdinger方程的傅里叶时间分解方法

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We prove an error estimate for a Lie–Trotter splitting operator associated with the Schr?dinger–Poisson equation in the semiclassical regime, when the WKB approximation is valid. In finite time, and so long as the solution to a compressible Euler–Poisson equation is smooth, the error between the numerical solution and the exact solution is controlled in Sobolev spaces, in a suitable phase/amplitude representation. As a corollary, we infer the numerical convergence of the quadratic observables with a time step independent of the Planck constant. A similar result is established for the nonlinear Schr?dinger equation in the weakly nonlinear regime.

机译：当WKB逼近有效时，我们证明了与在半经典状态下的Schr？dinger-Poisson方程相关的Lie-Trotter分裂算子的误差估计。在有限时间内，只要可压缩的Euler-Poisson方程的解是平滑的，就可以在Sobolev空间中以合适的相位/幅度表示形式控制数值解和精确解之间的误差。作为推论，我们用与普朗克常数无关的时间步长推论二次可观测量的数值收敛。对于弱非线性条件下的非线性薛定ding方程，建立了相似的结果。

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《SIAM Journal on Numerical Analysis》 |2013年第6期|共27页
作者
RéMI CARLES;
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正文语种 eng
中图分类数值分析;
关键词
Lie–Trotter splitting; nonlinear Schr?dinger equation; semiclassical limit; Burgers equation; hyperbolic equations;

机译：Lie-Trotter分裂;非线性Schrdinger方程;半经典极限;Burgers方程;双曲型方程;

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专利

1. ON FOURIER TIME-SPLITTING METHODS FOR NONLINEAR SCHR?DINGER EQUATIONS IN THE SEMICLASSICAL LIMIT~? [J] . RéMI CARLES SIAM Journal on Numerical Analysis . 2013,第6期

机译：半经典极限下非线性Schrüdinger方程的傅里叶时间分解方法
2. Convergence analysis of high-order time-splitting pseudospectral methods for nonlinear schr?dinger equations [J] . Thalhammer M. SIAM Journal on Numerical Analysis . 2012,第6期

机译：非线性薛定ding方程高阶时间分解伪谱方法的收敛性分析
3. Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schr?dinger equations [J] . Ameneh Taleei, Mehdi Dehghan Computer physics communications . 2014,第6期

机译：一维和多维非线性薛定ding方程孤子解的时分伪谱域分解方法
4. A Note on Non-radial Sign-changing Solutions for the Schr?dinger-Poisson Problem in the Semiclassical Limit [C] . Giusi Vaira School and Workshop on Cocompact Imbeddings, Profile Decompositions, and their Applicatons to PDE . 2013

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5. Development of level set methods for computing the semiclassical limit of Schrödinger equations with potentials [D] . Wang, Zhongming 2008

机译：开发水平集方法以计算具有势能的Schrödinger方程的半经典极限
6. Theory of quantum path computing with Fourier optics and future applications for quantum supremacy neural networks and nonlinear Schrödinger equations [O] . Burhan Gulbahar -1

机译：傅里叶光学的量子路径计算理论及其在量子至上神经网络和非线性Schrödinger方程中的未来应用
7. ON FOURIER TIME-SPLITTING METHODS FOR NONLINEAR SCHRÖDINGER EQUATIONS IN THE SEMICLASSICAL LIMIT∗ [O] . 2016

机译：关于半经典极限中非线性schrödinger方程的傅立叶时间分裂方法*

ON FOURIER TIME-SPLITTING METHODS FOR NONLINEAR SCHR?DINGER EQUATIONS IN THE SEMICLASSICAL LIMIT~?

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