General Higher-Order Breather and Hybrid Solutions of the Fokas System

作     者：Ting-Ting Chen Peng-Yan Hu Jing-Song He 陈婷婷;胡鹏彦;贺劲松

作者机构：Department of MathematicsNingbo UniversityNingbo315211China College of Mathematics and StatisticsShenzhen UniversityShenzhen518060China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2019年第71卷第5期

页      面：496-508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：Supported by the National Natural Science Foundation of China under Grant No.11671219 the Natural Science Foundation of Zhejiang Province under Grant No.LZ19A010001 the K.C.Wong Magna Fund in Ningbo University 

主　　题：Fokas system bilinear method breathers hybrid solutions 

摘      要：Fokas system is the simplest(2+1)-dimensional extension of the nonlinear Schr?dinger(NLS) equation(Eq.(2), Inverse Problems 10(1994) L19-L22). By appropriately limiting on soliton solutions generated by the Hirota bilinear method, the explicit forms of n-th breathers and semi-rational solutions for the Fokas system are derived. The obtained first-order breather exhibits a range of interesting dynamics. For high-order breather, it has more rich dynamical behaviors. The first-order and the second-order breather solutions are given graphically. Using the long wave limit in soliton solutions, rational solutions are obtained, which are used to analyze the mechanism of the rogue wave and lump respectively. By taking a long waves limit of a part of exponential functions in f and g appeared in the bilinear form of the Fokas system, many interesting hybrid solutions are constructed. The hybrid solutions illustrate various superposed wave structures involving rogue waves, lumps, solitons, and periodic line waves. Their rather complicated dynamics are revealed.