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Chin. Phys. B, 2020, Vol. 29(5): 050201    DOI: 10.1088/1674-1056/ab7e9d
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Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws

Xian-Guo Geng(耿献国), Fei-Ying Guo(郭飞英), Yun-Yun Zhai(翟云云)
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Abstract  With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2×2 matrix spectral problem is proposed, in which the first nontrivial member in the positive flows can be reduced to a new generalization of the Wadati-Konno-Ichikawa (WKI) equation. Further, a new generalization of the Fokas-Lenells (FL) equation is derived from the negative flows. Resorting to these two Lax pairs and Riccati-type equations, the infinite conservation laws of these two corresponding equations are obtained.
Keywords:  integrable generalizations      positive flow and negative flow      infinite conservation laws  
Received:  11 February 2020      Revised:  02 March 2020      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
  02.30.Ik (Integrable systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11971441, 11871440, and 11931017) and Key Scientific Research Projects of Colleges and Universities in Henan Province, China (Grant No. 20A110006).
Corresponding Authors:  Yun-Yun Zhai     E-mail:  zhaiyy@zzu.edu.cn

Cite this article: 

Xian-Guo Geng(耿献国), Fei-Ying Guo(郭飞英), Yun-Yun Zhai(翟云云) Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws 2020 Chin. Phys. B 29 050201

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