An N-breather solution and hybrid solutions of rogue wave and breather for complex mKdV equation

doi:10.1088/1674-1056/adcdef

中国物理B ›› 2025, Vol. 34 ›› Issue (7): 70202-070202.doi: 10.1088/1674-1056/adcdef

An N-breather solution and hybrid solutions of rogue wave and breather for complex mKdV equation

Wenjing Hu(胡文静) and Hasi Gegen(葛根哈斯)†

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

收稿日期:2025-02-20 修回日期:2025-04-12 接受日期:2025-04-17 出版日期:2025-06-18 发布日期:2025-07-03
通讯作者: Hasi Gegen E-mail:gegen@imu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12061051 and 12461048).

An N-breather solution and hybrid solutions of rogue wave and breather for complex mKdV equation

Wenjing Hu(胡文静) and Hasi Gegen(葛根哈斯)†

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received:2025-02-20 Revised:2025-04-12 Accepted:2025-04-17 Online:2025-06-18 Published:2025-07-03
Contact: Hasi Gegen E-mail:gegen@imu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12061051 and 12461048).

摘要/Abstract

摘要： A compact Grammian form for N-breather solution to the complex mKdV equation is derived using the bilinear Kadomtsev-Petviashvili hierarchy reduction method. The propagation trajectory, period, maximum points, and peak value of the 1-breather solution are calculated. Additionally, through the asymptotic analysis of 2-breather solution, we show that two breathers undergo an elastic collision. By applying the generalized long-wave limit method, the fundamental and second-order rogue wave solutions for the complex mKdV equation are obtained from the 1-breather and 2-breather solutions, respectively. We also construct the hybrid solution of a breather and a fundamental rogue wave for the complex mKdV equation from the 2-breather solution. Furthermore, the hybrid solution of two breathers and a fundamental rogue wave as well as the hybrid solution of a breather and a second-order rogue wave for the complex mKdV equation are derived from the 3-breather solution via the generalized long-wave limit method. By controlling the phase parameters of breathers, the diverse phenomena of interaction between the breathers and the rogue waves are demonstrated.

关键词: complex mKdV equation, hybrid solutions of breather and rogue wave, KP hierarchy reduction method, generalized long-wave limit method

Abstract: A compact Grammian form for N-breather solution to the complex mKdV equation is derived using the bilinear Kadomtsev-Petviashvili hierarchy reduction method. The propagation trajectory, period, maximum points, and peak value of the 1-breather solution are calculated. Additionally, through the asymptotic analysis of 2-breather solution, we show that two breathers undergo an elastic collision. By applying the generalized long-wave limit method, the fundamental and second-order rogue wave solutions for the complex mKdV equation are obtained from the 1-breather and 2-breather solutions, respectively. We also construct the hybrid solution of a breather and a fundamental rogue wave for the complex mKdV equation from the 2-breather solution. Furthermore, the hybrid solution of two breathers and a fundamental rogue wave as well as the hybrid solution of a breather and a second-order rogue wave for the complex mKdV equation are derived from the 3-breather solution via the generalized long-wave limit method. By controlling the phase parameters of breathers, the diverse phenomena of interaction between the breathers and the rogue waves are demonstrated.

Key words: complex mKdV equation, hybrid solutions of breather and rogue wave, KP hierarchy reduction method, generalized long-wave limit method

中图分类号: (Integrable systems)

02.30.Ik

05.45.Yv (Solitons) 52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)) 04.30.Nk (Wave propagation and interactions)

Wenjing Hu(胡文静) and Hasi Gegen(葛根哈斯). An N-breather solution and hybrid solutions of rogue wave and breather for complex mKdV equation[J]. 中国物理B, 2025, 34(7): 70202-070202.

Wenjing Hu(胡文静) and Hasi Gegen(葛根哈斯). An N-breather solution and hybrid solutions of rogue wave and breather for complex mKdV equation[J]. Chin. Phys. B, 2025, 34(7): 70202-070202.

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An N-breather solution and hybrid solutions of rogue wave and breather for complex mKdV equation

An N-breather solution and hybrid solutions of rogue wave and breather for complex mKdV equation

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