A discrete KdV equation hierarchy:continuous limit, diverse exact solutions and their asymptotic state analysis  

作　　者：Xue-Ke Liu Xiao-Yong Wen 

机构地区：[1]School of Applied Science,Beijing Information Science and Technology University,Beijing 100192,China

出　　处：《Communications in Theoretical Physics》2022年第6期1-14,共14页理论物理通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 12071042);the Beijing Natural Science Foundation (Grant No. 1202006)。

摘　　要：In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized(m, 2N-m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.

关 键 词：discrete KdV equation hierarchy continuous limit generalized(m 2N-m)-fold Darboux transformation exact solutions asymptotic analysis 

分 类 号：O175[理学—数学]