From breather solutions to lump solutions: A construction method for the Zakharov equation

doi:10.1088/1674-1056/acf706

中国物理B ›› 2023, Vol. 32 ›› Issue (12): 120201-120201.doi: 10.1088/1674-1056/acf706

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From breather solutions to lump solutions: A construction method for the Zakharov equation

Feng Yuan(袁丰)^1,†, Behzad Ghanbari², Yongshuai Zhang(张永帅)³, and Abdul Majid Wazwaz⁴

1 College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Department of Mathematics, Kermanshah University of Technology, Kermanshah, Iran;
3 Department of Mathematics, Shaoxing University, Shaoxing 312000, China;
4 Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

收稿日期:2023-07-16 修回日期:2023-08-23 接受日期:2023-09-06 出版日期:2023-11-14 发布日期:2023-11-27
通讯作者: Feng Yuan E-mail:yf2017@mail.ustc.edu.cn
基金资助:
This work is sponsored by NUPTSF (Grant Nos.NY220161 and NY222169), the Foundation of Jiangsu Provincial Double-Innovation Doctor Program (Grant No.JSSCBS20210541), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No.22KJB110004), and the National Natural Science Foundation of China (Grant No.12171433).

From breather solutions to lump solutions: A construction method for the Zakharov equation

Feng Yuan(袁丰)^1,†, Behzad Ghanbari², Yongshuai Zhang(张永帅)³, and Abdul Majid Wazwaz⁴

1 College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Department of Mathematics, Kermanshah University of Technology, Kermanshah, Iran;
3 Department of Mathematics, Shaoxing University, Shaoxing 312000, China;
4 Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA

Received:2023-07-16 Revised:2023-08-23 Accepted:2023-09-06 Online:2023-11-14 Published:2023-11-27
Contact: Feng Yuan E-mail:yf2017@mail.ustc.edu.cn
Supported by:
This work is sponsored by NUPTSF (Grant Nos.NY220161 and NY222169), the Foundation of Jiangsu Provincial Double-Innovation Doctor Program (Grant No.JSSCBS20210541), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No.22KJB110004), and the National Natural Science Foundation of China (Grant No.12171433).

摘要/Abstract

摘要： Periodic solutions of the Zakharov equation are investigated. By performing the limit operation λ_2l-1 to λ₁ on the eigenvalues of the Lax pair obtained from the n-fold Darboux transformation, an order-n breather-positon solution is first obtained from a plane wave seed. It is then proven that an order-n lump solution can be further constructed by taking the limit λ₁ to λ₀ on the breather-positon solution, because the unique eigenvalue λ₀ associated with the Lax pair eigenfunction Ψ(λ₀)=0 corresponds to the limit of the infinite-periodic solutions. A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.

关键词: Zakharov equation, breather solution, b-positon solution, lump solution

Abstract: Periodic solutions of the Zakharov equation are investigated. By performing the limit operation λ_2l-1 to λ₁ on the eigenvalues of the Lax pair obtained from the n-fold Darboux transformation, an order-n breather-positon solution is first obtained from a plane wave seed. It is then proven that an order-n lump solution can be further constructed by taking the limit λ₁ to λ₀ on the breather-positon solution, because the unique eigenvalue λ₀ associated with the Lax pair eigenfunction Ψ(λ₀)=0 corresponds to the limit of the infinite-periodic solutions. A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.

Key words: Zakharov equation, breather solution, b-positon solution, lump solution

中图分类号: (Integrable systems)

02.30.Ik

02.30.Jr (Partial differential equations) 05.45.-a (Nonlinear dynamics and chaos)

Feng Yuan(袁丰), Behzad Ghanbari, Yongshuai Zhang(张永帅), and Abdul Majid Wazwaz. From breather solutions to lump solutions: A construction method for the Zakharov equation[J]. 中国物理B, 2023, 32(12): 120201-120201.

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From breather solutions to lump solutions: A construction method for the Zakharov equation

From breather solutions to lump solutions: A construction method for the Zakharov equation

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