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Structure-preserving Gauss methods for the nonlinear Schrödinger equation
Calcolo ( IF 1.4 ) Pub Date : 2021-03-29 , DOI: 10.1007/s10092-021-00405-w
Georgios Akrivis , Dongfang Li

We use the scalar auxiliary variable (SAV) reformulation of the nonlinear Schrödinger (NLS) equation to construct structure-preserving SAV–Gauss methods for the NLS equation, namely \(L^2\)-conservative methods satisfying a discrete analogue of the energy (the Hamiltonian) conservation of the equation. This is in contrast to Gauss methods for the standard form of the NLS equation that are \(L^2\)-conservative but not energy-conservative. We also discuss efficient linearizations of the new methods and their conservation properties.



中文翻译:

非线性Schrödinger方程的保结构高斯方法。

我们使用非线性薛定ding(NLS)方程的标量辅助变量(SAV)重新构造,为NLS方程构造保留结构的SAV–Gauss方法,即满足能量离散模拟的\(L ^ 2 \)-守恒方法。 (哈密顿量)方程的守恒。这与NLS方程的标准形式的高斯方法相反,该方法是\(L ^ 2 \)守恒但不是能量守恒。我们还将讨论新方法的有效线性化及其守恒性质。

更新日期:2021-03-29
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