Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations

doi:10.1088/1674-1056/ac935b

中国物理B ›› 2023, Vol. 32 ›› Issue (4): 40201-040201.doi: 10.1088/1674-1056/ac935b

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Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations

Feng Yuan(袁丰)^1,† and Behzad Ghanbari²

1 College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Department of Basic Science, Kermanshah University of Technology, Kermanshah, Iran

收稿日期:2022-08-02 修回日期:2022-09-06 接受日期:2022-09-21 出版日期:2023-03-10 发布日期:2023-03-17
通讯作者: Feng Yuan E-mail:yf2017@mail.ustc.edu.cn,fengyuan@njupt.edu.cn
基金资助:
Project 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, China (Grant No. 22KJB110004), and the National Natural Science Foundation of China (Grant No. 11871446).

Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations

Feng Yuan(袁丰)^1,† and Behzad Ghanbari²

1 College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;
2 Department of Basic Science, Kermanshah University of Technology, Kermanshah, Iran

Received:2022-08-02 Revised:2022-09-06 Accepted:2022-09-21 Online:2023-03-10 Published:2023-03-17
Contact: Feng Yuan E-mail:yf2017@mail.ustc.edu.cn,fengyuan@njupt.edu.cn
Supported by:
Project 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, China (Grant No. 22KJB110004), and the National Natural Science Foundation of China (Grant No. 11871446).

摘要/Abstract

摘要： Solving nonlinear partial differential equations have attracted intensive attention in the past few decades. In this paper, the Darboux transformation method is used to derive several positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations. Based on the zero seed solution, the positon solution and the hybrid solutions of positon and soliton are constructed. The composition of positons is studied, showing that multi-positons of (2+1)-dimensional equations are decomposed into multi-solitons as well as the (1+1)-dimensions. Moreover, the interactions between positon and soliton are analyzed. In addition, the hybrid solutions of b-positon and breather are obtained using the plane wave seed solution, and their evolutions with time are discussed.

关键词: positon solution, b-positon solution, breather solution, the hybrid solution, the Darboux transformation

Abstract: Solving nonlinear partial differential equations have attracted intensive attention in the past few decades. In this paper, the Darboux transformation method is used to derive several positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations. Based on the zero seed solution, the positon solution and the hybrid solutions of positon and soliton are constructed. The composition of positons is studied, showing that multi-positons of (2+1)-dimensional equations are decomposed into multi-solitons as well as the (1+1)-dimensions. Moreover, the interactions between positon and soliton are analyzed. In addition, the hybrid solutions of b-positon and breather are obtained using the plane wave seed solution, and their evolutions with time are discussed.

Key words: positon solution, b-positon solution, breather solution, the hybrid solution, the Darboux transformation

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) and Behzad Ghanbari. Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations[J]. 中国物理B, 2023, 32(4): 40201-040201.

Feng Yuan(袁丰) and Behzad Ghanbari. Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations[J]. Chin. Phys. B, 2023, 32(4): 40201-040201.

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Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations

Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations

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