非线性薛定谔方程解的同伦分析
Solutions of the Non-Linear Schr?dinger Equation Based on the Homotopy Analysis Method
DOI: 10.12677/PM.2024.142051, PDF,    国家自然科学基金支持
作者: 徐 扬, 单 可, 梁雨珂, 吴颉尔, 周 昱*：江苏科技大学理学院，江苏 镇江；罗文琛：中南大学物理学院，湖南 长沙
关键词: 非线性薛定谔方程；孤子；周期解；同伦分析法；Nonlinear Schr?dinger Equation； Soliton； Periodic Solution； Homotopy Analysis Method
摘要: 同伦分析法是一种求解非线性演化方程的有效方法，本文研究了非线性薛定谔方程的同伦分析解。通过将方程化为耦合的方程组，给出了具有高次非线性和高阶色散的非线性薛定谔方程的孤子解和周期解，研究可给类似问题的求解提供有益思路。
Abstract: Homotopy analysis method is an effective method for solving nonlinear evolution equations. This paper studies the homotopy analysis solutions of nonlinear Schrödinger equations. By converting the equations into coupled equation groups, it gives soliton solution and periodic solution for the nonlinear Schrödinger equations with high-order nonlinearity and dispersion. The research may provide useful insights for solving similar equations.
文章引用：徐扬, 单可, 梁雨珂, 吴颉尔, 周昱, 罗文琛. 非线性薛定谔方程解的同伦分析[J]. 理论数学, 2024, 14(2): 527-538. https://doi.org/10.12677/PM.2024.142051

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