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The Riemann–Hilbert approach to the generalized second-order flow of three-wave hierarchy
Applicable Analysis ( IF 1.1 ) Pub Date : 2021-03-29 , DOI: 10.1080/00036811.2021.1906414
Deng-Shan Wang 1 , Xiao-Yong Wen 2
Affiliation  

This paper extends the second-order three-wave flow of Fordy and Kulish to propose a generalized second-order flow of the three-wave hierarchy. Then the Lax pair of the generalized second-order three-wave flow is constructed by the standard prolongation technique, and the infinite conservation laws for this flow are derived. Finally, the Riemann–Hilbert approach is applied to the initial value problem of this flow, and the N-soliton solutions to the second-order three-wave flow are derived explicitly. Collision behaviors of the two and three solitons are demonstrated graphically, which shows that our results have potential applications to the resonant three-wave interactions in nonlinear media.



中文翻译:

三波层次的广义二阶流的黎曼-希尔伯特方法

本文扩展了Fordy和Kulish的二阶三波流,提出了三波层次的广义二阶流。然后用标准延长技术构造广义二阶三波流的Lax对,并推导出该流的无限守恒定律。最后,将Riemann-Hilbert方法应用于该流的初值问题,明确导出了二阶三波流的N-孤子解。以图形方式展示了两个和三个孤子的碰撞行为,这表明我们的结果对非线性介质中的共振三波相互作用具有潜在的应用。

更新日期:2021-03-29
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