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：

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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。