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

作     者：Xian-Guo Geng Fei-Ying Guo Yun-Yun Zhai 耿献国;郭飞英;翟云云

作者机构：School of Mathematics and StatisticsZhengzhou UniversityZhengzhou 450001China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2020年第29卷第5期

页      面：70-73页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11971441,11871440,and 11931017) Key Scientific Research Projects of Colleges and Universities in Henan Province,China(Grant No.20A110006) 

主　　题：integrable generalizations positive flow and negative flow infinite conservation laws 

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.