Darboux transformation and rogue wave solutions for the variable-coefficients coupled Hirota equations

详细信息    查看全文

• 作者：Xin Wang^a ; ^b ; ^{wangxinlinzhou@163.com} ; Chong Liu^c ; ^d ; Lei Wang^e
• 关键词：Integrable system ; Darboux transformation ; Rogue wave ; Variable-coefficients coupled Hirota equations
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1534-1552
• 全文大小：1364 K
• 卷排序：449

文摘

We construct the Lax pair and Darboux transformation for the variable-coefficients coupled Hirota equations. Based on modulation instability and by taking the limit approach, we derive two types of Nth-order rogue wave solutions with different dynamic structures in compact determinant representations. The explicit first-order rogue wave solution is presented, prolific vector rogue-wave patterns such as the dark-bright, composite, three-sister, quadruple and sextuple rogue waves with multiple compression points are demonstrated. In particular, in contrast to the standard Peregrine combs, unusual vector rogue wave combs such as the dark-bright and composite rogue wave combs are revealed by choosing sufficiently large periodic modulation amplitudes. Further, some wave characteristics such as the difference between light intensity and continuous wave background, and pulse energy evolution of the dark rogue wave solution that features multiple compression points are discussed in detail.