非线性薛定谔方程中呼吸子的Splitting解法
Breather in Nonlinear Schrödinger Equation by the Splitting Method
DOI: 10.12677/pm.2024.1411369, PDF,    国家自然科学基金支持
作者: 段星星, 樊 炜：江苏科技大学理学院，江苏 镇江
关键词: 非线性薛定谔方程；Splitting方法；离散傅利叶变换；Nonlinear Schrödinger Equation； Splitting Method； Discrete Fourier Transform
摘要: 呼吸子是非线性薛定谔方程(NLSE)中的一类重要的解，在量子力学、光学和数学物理中具有重要应用。方程的非线性项使得其解析求解非常复杂，因此数值求解方法常用来模拟方程的行为。Splitting方法是一种对非线性薛定谔方程具有很高效率的算法，本文简单介绍splitting方法，然后用其求解了一种常见的呼吸子。通过splitting方法求解呼吸子，可以深入理解其在不同参数条件下的演化行为，为相关实验和应用提供理论支持。
Abstract: The Nonlinear Schrödinger Equation (NLSE) plays a crucial role in quantum mechanics, optics, and mathematical physics. Breather is one type of soliton solutions of NLSE. The nonlinearity of the equation makes it hard to obtain the analytic solution of the breather. Numerical methods are usually adopted to simulate the behavior of the solitons, one of which is the splitting method. In this paper, we use the splitting method to simulate one kind of breather solutions. By this way, we can gain a deeper understanding of their evolutionary behavior under varying parameter conditions, thereby providing theoretical support for related experiments and applications.
文章引用：段星星, 樊炜. 非线性薛定谔方程中呼吸子的Splitting解法[J]. 理论数学, 2024, 14(11): 10-16. https://doi.org/10.12677/pm.2024.1411369

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