标题： 薛定谔方程的指数三次B样条有限元方法数值研究 显示英文标题

标题： Numerical investigation of the solutions of Schrodinger equation with exponential cubic B-spline finite element method

摘要： 本文研究了三次非线性 Schrodinger 方程的数值解，采用指数 B 样条配置法。目标方程的时间离散化使用了 Crank-Nicolson 公式。为了数值计算的目的，还采用了线性化技术。作为测试问题，考虑了四个数值例子：单孤子、相向运动的两个孤子的碰撞、驻定孤子和移动孤子的产生以及束缚态解。通过最大误差范数和守恒常量来衡量所提出方法的精度和效率。所得结果与可能的解析值以及一些早期研究中的结果进行了比较。 显示英文摘要

摘要： 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.