四阶非线性Schro¨dinger方程几乎质量守恒的低正则算法
A Low-Regularity Integrator for the Fourth-Order Nonlinear Schro¨dinger Equation with Almost Mass Conservation
DOI: 10.12677/PM.2022.1210177, PDF, HTML, 下载: 161  浏览: 247  国家自然科学基金支持
作者: 宁 翠：广东金融学院金融数学与统计学院, 广东 广州
关键词: 四阶非线性Schro¨dinger方程；低正则；一阶收敛；质量守恒；Fourth-Order Nonlinear Schro¨dinger Equation； Low-Regularity Integrator； First-Order Convergent； Mass Conversation
摘要: 本文研究了四阶非线性Schro¨dinger方程的具有几乎质量守恒的一种低正则算法.该算法不仅保持一阶收敛, 并且还具有几乎质量守恒性. 我们通过严格的误差分析,证明了当初值属于Hγ+3(Td)时, 对固定的T > 0和γ > d/2, 存在常C=C(||u||L∞ (0,T;Hγ+3))> 0,使得其中un是四阶非线性Schro¨dinger方程在tn=nτ时的数值解. 此外, 数值解的质量M(un)满足
Abstract: In this paper, we introduce a low-regularity integrator for the fourth-order nonlinear Schro¨dinger equation with almost mass conservation. The algorithm can not only achieve first-order convergence, but also obey almost mass conservation law. By rigorous error analysis, for rough initial data in Hγ+3(Td) with γ > d/2, up to some fixed time of T , there exists C=C(||u||L∞ (0,T;Hγ+3))> 0, such that where un denotes the numerical solution at tn=nτ. Moreover, the mass of the numerical solution M(un) verifies
文章引用：宁翠. 四阶非线性Schro¨dinger方程几乎质量守恒的低正则算法[J]. 理论数学, 2022, 12(10): 1636-1648. https://doi.org/10.12677/PM.2022.1210177

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