五阶可积非线性薛定谔方程的分子波
The Molecular Waves of Fifth-Order Integrable Nonlinear Schr?dinger Equation
摘要: 本文我们研究了五阶非线性薛定谔方程中的呼吸子分子及其态转换机制。基于达布变换方法，给出了方程的二阶呼吸子解，当两个呼吸子的群速度共振时，会形成一个稳定的束缚态结构，即呼吸子分子。我们讨论了呼吸子分子中呼吸子原子发生态转换的条件，得到了不同类型的转换波分子。最后我们分析了相位参数θ2和μ2对转换波原子的形状以及位置的影响。
Abstract: In this paper, we study the breather molecule and its state transition mechanism in the fifth-order integrable nonlinear Schrödinger equation. Based on the Darboux transformation method, the second-order breather solution of the equation is given, where a stable structure of bound states, i.e., the breather molecule, is formed when the group velocities of two breathers resonate. We discuss the transition conditions for the breather atoms in the breather molecule and obtain different types of transition wave molecules. Finally, we analyze the effects of the phase parameters θ2 and μ2 on the shape as well as the position of the transition wave atoms.
文章引用：赵俊飞. 五阶可积非线性薛定谔方程的分子波[J]. 应用数学进展, 2022, 11(3): 1320-1325. https://doi.org/10.12677/AAM.2022.113144

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