We construct an efficient numerical scheme for the coupled nonlinear Schrödinger equations by using adaptive spline function. We use the Crank–Nicolson scheme to discretize the time variables and the adaptive spline function to discretize spatial variables. The problem is reduced to a system of matrix equation iteration. We theoretically give stability analysis and numerically prove the law of conservation of energy. Numerical simulations are performed to demonstrate the effectiveness of the method.

中文翻译：

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耦合非线性薛定谔方程的有效样条方案

我们通过使用自适应样条函数为耦合非线性薛定谔方程构建了一个有效的数值方案。我们使用 Crank-Nicolson 方案来离散时间变量，并使用自适应样条函数来离散空间变量。问题被简化为一个矩阵方程迭代系统。我们从理论上给出了稳定性分析并数值证明了能量守恒定律。进行数值模拟以证明该方法的有效性。