Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton

doi:10.1088/1674-1056/ad1822

中国物理B ›› 2024, Vol. 33 ›› Issue (4): 40202-040202.doi: 10.1088/1674-1056/ad1822

Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton

Qiao-Hong Han(韩巧红) and Man Jia(贾曼)^†

School of Physical Science and Technology, Ningbo University, Ningbo 315211, China

收稿日期:2023-11-20 修回日期:2023-12-15 接受日期:2023-12-22 出版日期:2024-03-19 发布日期:2024-03-27
通讯作者: Man Jia E-mail:jiaman@nbu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12275144, 12235007, and 11975131) and K. C. Wong Magna Fund in Ningbo University. The authors acknowledge Professor S. Y. Lou for helpful discussion.

Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton

Qiao-Hong Han(韩巧红) and Man Jia(贾曼)^†

School of Physical Science and Technology, Ningbo University, Ningbo 315211, China

Received:2023-11-20 Revised:2023-12-15 Accepted:2023-12-22 Online:2024-03-19 Published:2024-03-27
Contact: Man Jia E-mail:jiaman@nbu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12275144, 12235007, and 11975131) and K. C. Wong Magna Fund in Ningbo University. The authors acknowledge Professor S. Y. Lou for helpful discussion.

摘要/Abstract

摘要： Integrable systems play a crucial role in physics and mathematics. In particular, the traditional (1+1)-dimensional and (2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions. Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from (1+1)-dimensional integrable systems by using a deformation algorithm. Here we establish a new (2+1)-dimensional Chen—Lee—Liu (C—L—L) equation using the deformation algorithm from the (1+1)-dimensional C—L—L equation. The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the (1+1)-dimension. It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C—L—L equation and its reciprocal transformation. The traveling wave solutions are derived in implicit function expression, and some asymmetry peakon solutions are found.

关键词: higher dimensional Chen—Lee—Liu equation, Lax integrable system, deformation algorithm, implicit traveling wave solutions

Abstract: Integrable systems play a crucial role in physics and mathematics. In particular, the traditional (1+1)-dimensional and (2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions. Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from (1+1)-dimensional integrable systems by using a deformation algorithm. Here we establish a new (2+1)-dimensional Chen—Lee—Liu (C—L—L) equation using the deformation algorithm from the (1+1)-dimensional C—L—L equation. The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the (1+1)-dimension. It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C—L—L equation and its reciprocal transformation. The traveling wave solutions are derived in implicit function expression, and some asymmetry peakon solutions are found.

Key words: higher dimensional Chen—Lee—Liu equation, Lax integrable system, deformation algorithm, implicit traveling wave solutions

中图分类号: (Integrable systems)

02.30.Ik

02.30.Jr (Partial differential equations)

Qiao-Hong Han(韩巧红) and Man Jia(贾曼). Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton[J]. 中国物理B, 2024, 33(4): 40202-040202.

Qiao-Hong Han(韩巧红) and Man Jia(贾曼). Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton[J]. Chin. Phys. B, 2024, 33(4): 40202-040202.

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Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton

Higher-dimensional Chen—Lee—Liu equation and asymmetric peakon soliton

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