Rogue waves on the periodic background in the high-order discrete mKdV equation

被引：4
|
作者：
Zhen, Yanpei [1 ]
Chen, Jinbing [1 ]
机构：
[1] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China
来源：
NONLINEAR DYNAMICS | 2023年 / 111卷 / 13期
关键词：
Rogue waves; Algebraic solitons; Travelling periodic waves; Darboux transformation; TRACE IDENTITY;
D O I：
10.1007/s11071-023-08481-z
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
We construct new exact solutions for the high-order discrete mKdV (dmKdV) equation. The exact solutions are obtained by using the nonlinearization of spectral problem, one-, and two-fold Darboux transformations. Two families of traveling periodic waves of the high-order dmKdV equation are expressed by the Jacobi dnoidal and cnoidal elliptic functions. Since the dnoidal traveling wave is modulationally stable and the traveling cnoidal wave is modulationally unstable, the rogue waves only generated on the cnoidal wave background while the algebraic solitons propagating on the dnoidal wave background.
引用
收藏
页码：12511 / 12524
页数：14
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