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

doi:10.1088/1674-1056/ab7e9d

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

[1]	Lax P D 1968 Commun. Pur. Appl. Math. 21 467
[2]	Ablowitz M J, Kaup D J, Newell A C and Segur H 1974 Stud. Appl. Math. 53 249
[3]	Shimizu T and Wadati M 1980 Prog. Theor. Phys. 63 808
[4]	Tchokouansi H T, Keutche V K and Kofane T C 2014 J. Math. Phys. 55 123511
[5]	Xiao Y 1990 Phys. Lett. A. 149 369
[6]	Geng X G, Li R M and Xue B 2020 J. Nonlinear Sci.
[7]	Geng X G and Lv Y Y 2012 Nonlinear Dynam. 69 1621
[8]	Li R M and Geng X G 2020 Stud. Appl. Math. 144 164
[9]	Wei J, Geng X G and Zeng X 2019 Trans. Amer. Math. Soc. 371 1483
[10]	Geng X G, Zhai Y Y and Dai H H 2014 Adv. Math. 263 123
[11]	Xu S Q and Geng X G 2018 Chin. Phys. B 27 120202
[12]	Geng X G and Liu H 2018 J. Nonlinear Sci. 28 739
[13]	Lou S Y and Lin J 2018 Chin. Phys. Lett. 35 050202
[14]	Liu Y K and Li B 2017 Chin. Phys. Lett. 34 010202
[15]	Geng X G and Li F 2009 Chin. Phys. Lett. 26 050201
[16]	Geng X G and Wang H 2014 Chin. Phys. Lett. 31 070202
[17]	Wadati M, Konno K and Ichikawa Y H 1979 J. Phys. Soc. Jpn. 47 1698
[18]	Ishimori Y A 1982 J. Phys. Soc. Jpn. 51 3036
[19]	Geng X G and Zhai Y Y 2018 Chin. Phys. B 27 040201
[20]	Xu X X 2002 Phys. Lett. A 301 250
[21]	Zhu H Y, Yu S M, Shen S F and Ma W X 2015 Commun. Nonlinear Sci. Numer. Simulat. 22 1341
[22]	Boiti M, Pempinelli F and Tu G Z 1983 Prog. Theor. Phys. 69 48
[23]	Zhang Y S, Qiu D Q, Cheng Y and He J S 2017 Theoret. Math. Phys. 191 710
[24]	Li Z, Geng X G and Guan L 2016 Math. Meth. Appl. Sci. 39 734
[25]	Zhang Y S, Rao J G, Cheng Y and He J S 2019 Physica D 399 173
[26]	Van Gorder R A 2012 Prog. Oret. Phys. 128 993
[27]	Zhang Y S, Qiu D Q, Mihalache D and He J S 2018 Chaos 28 103108
[28]	Zhang Y S and Xu S W 2020 Appl. Math. Lett. 99 105995
[29]	Vekslerchik V E 2011 Nonlinearity 24 1165
[30]	Lenells J and Fokas A S 2009 Nonlinearity 22 11

[1]	An extension of integrable equations related to AKNS and WKI spectral problems and their reductions Xian-Guo Geng(耿献国), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2018, 27(4): 040201.
[2]	Integrability of extended (2+1)-dimensional shallow water wave equation with Bell polynomials Wang Yun-Hu (王云虎), Chen Yong (陈勇). Chin. Phys. B, 2013, 22(5): 050509.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention