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Higher-order semirational solutions and W-shaped solitons for the multi-component AB system
Wave Motion ( IF 2.4 ) Pub Date : 2021-06-08 , DOI: 10.1016/j.wavemoti.2021.102790
Tao Xu , Guoliang He

The multi-component AB system, which appears in the ultra-short optical pulse field and the geophysical fluid dynamics, is investigated via the Darboux transformation technique. Combining the special vector solutions for the Lax pair and the corresponding Darboux transformation, the higher-order semirational solutions for the AB system are constructed. Besides, the semirational solutions are discussed in three different types: (1) the degenerate case that higher-order rogue waves (RWs); (2) higher-order RWs coexisting with multi bright and dark solitons; (3) higher-order RWs coexisting with multi breathers. Through studying the modulation instability analysis for the AB system, some higher-order W-shaped solitons are constructed when the modulation instability growth rate becomes zero. It is interesting that the first- and second-order W-shaped solitons in the last components q, r and s are the plane waves, and the normal W-shaped solitons exist in not less than third order case.



中文翻译:

多分量 AB 系统的高阶半有理解和 W 形孤子

通过达布变换技术研究了超短光脉冲场和地球物理流体动力学中出现的多分量AB系统。结合 Lax 对的特殊向量解和相应的 Darboux 变换,构造了 AB 系统的高阶半有理解。此外,半有理解被分为三种不同的类型讨论:(1)高阶流氓波(RWs)的退化情况;(2) 高阶RWs与多种明暗孤子共存;(3) 高阶 RW 与多个呼吸器共存。通过研究AB系统的调制不稳定性分析,当调制不稳定性增长率为零时,构造了一些高阶W形孤子。q, r 是平面波,正常的 W 形孤子至少在三阶情况下存在。

更新日期:2021-06-15
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