非局域正流短脉冲方程解的长时间渐近

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 108-129.

非局域正流短脉冲方程解的长时间渐近

刘文豪^*(), 张玉峰()

中国矿业大学数学学院江苏徐州 221116

收稿日期:2024-10-15 修回日期:2025-02-17 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 刘文豪 E-mail:wenhao_1003@163.com;zhangyfcumt@163.com
作者简介:张玉峰, Email: zhangyfcumt@163.com
基金资助:
国家自然科学基金(12501336);国家自然科学基金(12371256)

Long-Time Asymptotics of the Nonlocal Positive Flow Short-Pules Equation

Wenhao Liu^*(), Yufeng Zhang()

School of Mathematics, China University of Mining and Technology, Jiangsu Xuzhou 221116

Received:2024-10-15 Revised:2025-02-17 Online:2026-02-26 Published:2026-01-19
Contact: Wenhao Liu E-mail:wenhao_1003@163.com;zhangyfcumt@163.com
Supported by:
NSFC(12501336);NSFC(12371256)

摘要/Abstract

摘要：

基于弹性梁在张力作用下的非线性横向振荡现象, 非局域正流短脉冲方程首次被提出. 通过非线性最速下降方法, 该方程的 Cauchy 问题解的长时间渐近行为被讨论. 从其所满足的 WKI 型 Lax 对出发, 相应的初始 Riemann-Hilbert 问题以及解的重构公式被建立. 经过转向、延拓、截断以及缩放平移这一系列对跳跃围线的形变, 从而将初始 Riemann-Hilbert 问题转变为可用抛物柱面函数求解的模型 Riemann-Hilbert 问题. 最终, 非局域正流短脉冲方程解的长时间渐近行为被得到.

关键词: 可积系统, 非线性最速下降方法, 长时间渐近

Abstract:

The nonlocal positive flow short-pules equation is first proposed based on the nonlinear transverse oscillation of elastic beam under tension in physics. By the nonlinear steepest descent method, the long-time asymptotics of the solution of the Cauchy problem for the equation is discussed. Starting from the WKI-type Lax pair it satisfies, the corresponding basic Riemann-Hilbert problem and reconstruction formula for the solution are established. Through a series of deformations such as reorientation, extending, cuting and rescaling, the basic Riemann-Hilbert problem is transformed into the model Riemann-Hilbert problem that can be solved using parabolic cylinder functions. Finally, the long-time asymptotics of the solution of the nonlocal positive flow short-pules equation is obtained.

Key words: integrable system, nonlinear steepest descent method, long-time asymptotics

中图分类号:

O175.24

刘文豪, 张玉峰. 非局域正流短脉冲方程解的长时间渐近[J]. 数学物理学报, 2026, 46(1): 108-129.

Wenhao Liu, Yufeng Zhang. Long-Time Asymptotics of the Nonlocal Positive Flow Short-Pules Equation[J]. Acta mathematica scientia,Series A, 2026, 46(1): 108-129.

图/表 5

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