2020
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*

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 corr… Show more

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Cited by 6 publications
(2 citation statements)
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“…[21][22][23][24][25] It is well known that searching for new integrable equations that possess N-solution solutions is one of the most significant subjects in the theory of integrable system. [26][27][28][29][30][31] In this paper, we propose a novel generalized FL equation…”
Section: Introductionmentioning
confidence: 99%
“…[21][22][23][24][25] It is well known that searching for new integrable equations that possess N-solution solutions is one of the most significant subjects in the theory of integrable system. [26][27][28][29][30][31] In this paper, we propose a novel generalized FL equation…”
Section: Introductionmentioning
confidence: 99%
“…Integrable systems obtained from negative flows have important physical and mathematical significance, such as the Camassa-Holm (CH) equation, the Degasperis-Procesi (DP) equation and the Vakhnenko equation. A mixed WKI-SP model has been found by combining the positive flows and extend the WKI hierarchy to incorporate negative flows [21,22].…”
Section: Introductionmentioning
confidence: 99%