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.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12061051 and 12461048).
Corresponding Authors:
Hasi Gegen
E-mail: gegen@imu.edu.cn
Cite this article:
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 2025 Chin. Phys. B 34 070202
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