（2+1）维Boiti-Leon-Pempinelli方程的新相干结构与混沌斑图

刘常福

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（2+1）维Boiti-Leon-Pempinelli方程的新相干结构与混沌斑图

更新时间：2026-10-29

- （2+1）维Boiti-Leon-Pempinelli方程的新相干结构与混沌斑图
- New Coherent Structures and Chaotic Patterns for the (2+1)-Dimensional Boiti-Leon-Pempinelli Equation
- 武汉大学学报自然科学英文版 2026年页码：1-8
- 作者机构：
  
  文山学院人工智能学院，云南文山 663099
- 作者简介：
  
  LIU Changfu, male, Professor, research direction: nonlinear partial differential equations. Email: chfuliu@163.com
- 基金信息：
  
  the National Natural Science Foundation of China(12261053);the Scientific Research Foundation of Department of Education of Yunnan Province(2022J0946)
- DOI：
  中图分类号： O175.29
- 收稿：2025-11-01，
  
  网络首发：2026-10-29，
- 稿件说明：
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刘常福.（2+1）维Boiti-Leon-Pempinelli方程的新相干结构与混沌斑图[J].武汉大学学报自然科学英文版,

LIU Changfu.New Coherent Structures and Chaotic Patterns for the (2+1)-Dimensional Boiti-Leon-Pempinelli Equation[J].Wuhan University Journal of Natural Sciences,
刘常福.（2+1）维Boiti-Leon-Pempinelli方程的新相干结构与混沌斑图[J].武汉大学学报自然科学英文版, DOI：https://doi.org/10.1051/wujns/001.

LIU Changfu.New Coherent Structures and Chaotic Patterns for the (2+1)-Dimensional Boiti-Leon-Pempinelli Equation[J].Wuhan University Journal of Natural Sciences, DOI：https://doi.org/10.1051/wujns/XXXXXXXX001.

摘要

（2+1）维Boiti-Leon-Pempinelli（BLP）方程具有可积性，且存在大量超越经典孤子的相干结构，但这类结构难以通过系统性方法推导得到。本文将辅助方程映射法与齐次平衡法相结合，得到了含两个任意函数的可分离变量解。借助这两个任意函数，本文在同一框架内构造了呼吸双孤子、对称呼吸孤子与双周期波。对相应势场的分析进一步表明，由奇异流形可诱导出分形怪波、分形dromion与混沌斑图。可见，任意函数的选取直接决定所得的动力学行为，这有助于阐明BLP方程的相干机制。

Abstract

The (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) equation is integrable and admits a wide class of coherent structures beyond classical solitons

but such structures are difficult to derive systematically. Combining the auxiliary equation mapping method with the homogeneous balance method

we obtain variable separation solutions that contain two arbitrary functions. These functions allow breather double solitons

symmetric breather solitons and double-period waves to be constructed within one scheme. Analysis of the associated potential field

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121313254&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=121313232&type=

10.15999985

2.96333337

further gives fractal rogue waves

fractal dromions and chaotic patterns generated by singular manifolds. The results relate the choice of arbitrary functions directly to the resulting dynamics and clarify the coherence mechanisms of the BLP system.

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references

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