数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2183-2195.
广义耦合导数非线性薛定谔方程的孤子分子、孤子共振以及 breather-positon 解
曾平平1(
), 曾平安2(), 许国安3,*()
- 1
浙江金融职业学院信息技术学院 杭州 310000
2浙江工业大学之江学院理学院 浙江绍兴 312000
3华侨大学数学科学学院 福建泉州 362021
-
收稿日期:2025-07-27修回日期:2026-03-26出版日期:2026-12-26发布日期:2026-08-14 -
通讯作者:许国安 E-mail:1360544995@qq.com;460877822@qq.com;xga99163@163.com -
作者简介:曾平平, E-mail: 1360544995@qq.com;
曾平安, E-mail: 460877822@qq.com -
基金资助:国家自然科学基金(12271096);福建省自然科学基金(2025J01165)
Soliton Molecules, Soliton Resonances and Breather Positon Solutions for the General Coupled Derivative Nonlinear Schrödinger Equation
Pingping Zeng1(), Pingan Zeng2(), Guoan Xu3,*()
- 1
Institute of Information Technology ,Zhejiang Financial College Hangzhou 310000
2School of Science ,Zhijiang College of Zhejiang University of Technology Zhejiang Shaoxing 312000
3School of Mathematical Sciences ,Huaqiao University Fujian Quanzhou 362021
-
Received:2025-07-27Revised:2026-03-26Online:2026-12-26Published:2026-08-14 -
Contact:Guoan Xu E-mail:1360544995@qq.com;460877822@qq.com;xga99163@163.com -
Supported by:NSFC(12271096);NSFFP(2025J01165)
摘要：
该文聚焦于广义耦合导数非线性薛定谔方程, 该方程以窄脉冲的非线性自变陡特性为显著特征. 基于 Lax 对, 构建行列式形式的
中图分类号:
- O175.29
引用本文
曾平平, 曾平安, 许国安. 广义耦合导数非线性薛定谔方程的孤子分子、孤子共振以及 breather-positon 解[J]. 数学物理学报, 2026, 46(6): 2183-2195.
Pingping Zeng, Pingan Zeng, Guoan Xu. Soliton Molecules, Soliton Resonances and Breather Positon Solutions for the General Coupled Derivative Nonlinear Schrödinger Equation[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2183-2195.
图1
2-孤子分子, 参数为 $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $c_1=1+{\rm i}$, $c_2=1$, $c_3=1$, $m_1=\frac{1}{2}$, $n_1=1$, $m_2=\frac{3}{2}$, $n_2=\sqrt{3}$."
图2
2-孤子分子, 参数为 $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $c_1=1+\frac{{\rm i}}{2}$, $c_2=1$, $c_3=1$, $m_1=\frac{\sqrt{2}}{2}$, $n_1=\frac{\sqrt{3}}{2}$, $m_2=1$, $n_2=\frac{\sqrt{5}}{2}$."
图3
3-孤子分子, 参数为 $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $c_1=1+{\rm i}$, $c_2=1$, $c_3=1$, $m_1=1$, $n_1=-1$, $m_2=\frac{1}{2}$, $n_2=\frac{1}{2}$, $m_3=2$, $n_3=-2$."
图4
3-孤子分子, 参数为 $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $c_1=1+{\rm i}$, $c_2=1$, $c_3=1$, $m_1=1$, $n_1=\frac{1}{2}$, $m_2=\frac{\sqrt{6}}{2}$, $n_2=\frac{3}{2}$, $m_3=\frac{\sqrt{2}}{2}$, $n_3=\frac{\sqrt{5}}{2}$."
图5
2-孤子分子与 1-暗孤子的孤子共振, 参数为 $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $c_1=1+{\rm i}$, $c_2=1$, $c_3=1$, $m_1=1$, $n_1=-1$, $m_2=\frac{2}{3}$, $n_2=-1$, $m_3=-\frac{1}{4}$, $n_3=\frac{1}{2}$."
图6
2-孤子分子与 1-类呼吸子型孤子的孤子共振, 参数为 $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $c_1=1+{\rm i}$, $c_2=1$, $c_3=1$, $m_1=\frac{1}{10}$, $n_1=\frac{3}{10}$, $m_2=\frac{4}{5}$, $n_2=-1$, $m_3=-\frac{1}{5}$, $n_3=1$."
图7
一阶 breather-positon 解, 参数为 $a_1=1$, $a_2=1$, $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $m_1=1$, $n_1=-1$."
图8
一阶 breather-positon 解, 参数为 $a_1=1$, $a_2=1$, $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $m_1=1$, $n_1=-\frac{1}{2}$."
图9
一阶 breather-positon 演化为类怪波过程,参数与图8相同."
图10
二阶 breather-positon 解, 参数为 $a_1=1$, $a_2=1$, $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $m_1=1$, $n_1=-1$, $p_k=0$, $q_k=0$."
图11
二阶 breather-positon 解, 参数为 $a_1=1$, $a_2=1$, $a=\frac{1}{2}$, $b=1+{\rm i}$, $c=\frac{1}{2}$, $m_1=1$, $n_1=-1$, $p_k=200$, $q_k=200$."
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