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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Wang, Xin^1,2  Liu, Chong^3,4  Wang, Lei⁵ 

[1] Zhongyuan Univ Technol, Coll Sci, Zhengzhou 450007, Peoples R China

[2] Zhengzhou Univ, Sch Math & Stat, 100 Kexue Rd, Zhengzhou 450001, Henan, Peoples R China

[3] Northwest Univ, Sch Phys, Xian 710069, Peoples R China

[4] Shaanxi Key Lab Theoret Phys Frontiers, Xian 710069, Peoples R China

[5] North China Elect Power Univ, Dept Math & Phys, Beijing 102206, Peoples R China

关键词: Integrable system;    Darboux transformation;    Rogue wave;    Variable-coefficients coupled Hirota equations;   

DOI  :  10.1016/j.jmaa.2016.12.079

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free