In this paper, we investigate the numerical solutions of the cubic nonlinear Schrodinger equation via the exponential B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A linearization technique is also employed for the numerical purpose. Four numerical examples related to single soliton, collision of two solitons that move in opposite directions, the birht of standing and mobile solitons and bound state solution are considered as the test problems. The accuracy and the efficiency of the purposed method are measured by max error norm and conserved constants. The obtained results are compared with the possible analytical values and those in some earlier studies.

中文翻译：

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指数三次B样条有限元法对薛定谔方程解的数值研究

在本文中，我们通过指数 B 样条搭配方法研究了三次非线性薛定谔方程的数值解。Crank-Nicolson 公式用于目标方程的时间离散化。线性化技术也用于数值目的。四个与单个孤子、两个相反方向运动的孤子碰撞、站立和移动孤子的产生以及束缚态解相关的数值例子被认为是测试问题。目标方法的准确性和效率通过最大误差范数和守恒常数来衡量。将获得的结果与可能的分析值和一些早期研究中的值进行比较。