Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws

doi:10.1088/1674-1056/ab7e9d

中国物理B ›› 2020, Vol. 29 ›› Issue (5): 50201-050201.doi: 10.1088/1674-1056/ab7e9d

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 下一篇

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

收稿日期:2020-02-11 修回日期:2020-03-02 出版日期:2020-05-05 发布日期:2020-05-05
通讯作者: Yun-Yun Zhai E-mail:zhaiyy@zzu.edu.cn
基金资助:
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).

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

Received:2020-02-11 Revised:2020-03-02 Online:2020-05-05 Published:2020-05-05
Contact: Yun-Yun Zhai E-mail:zhaiyy@zzu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: integrable generalizations, positive flow and negative flow, infinite conservation laws

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.

Key words: integrable generalizations, positive flow and negative flow, infinite conservation laws

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems)

耿献国, 郭飞英, 翟云云. Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws[J]. 中国物理B, 2020, 29(5): 50201-050201.

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[J]. Chin. Phys. B, 2020, 29(5): 50201-050201.

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[1]	耿献国, 翟云云. An extension of integrable equations related to AKNS and WKI spectral problems and their reductions[J]. 中国物理B, 2018, 27(4): 40201-040201.
[2]	王云虎, 陈勇. Integrability of extended (2+1)-dimensional shallow water wave equation with Bell polynomials[J]. 中国物理B, 2013, 22(5): 50509-050509.

Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws

Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws

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