数学
守恒定律
可积系统
本征函数
转化(遗传学)
极限(数学)
松驰对
数学分析
孤子
达布积分
特征向量
非线性系统
物理
几何学
量子力学
生物化学
化学
基因
曲率
作者
Hai‐qiong Zhao,Tong Zhou
出处
期刊:Nonlinearity
[IOP Publishing]
日期:2021-08-05
卷期号:34 (9): 6450-6472
被引量:5
标识
DOI:10.1088/1361-6544/ac15ab
摘要
Abstract The intimate connection between discrete and continuous integrable systems may yield deep insight into some inherent discreteness of physical phenomena. In this paper, a spatially discrete Boussinesq equation is investigated. The integrability of the spatially discrete model is confirmed by showing the existence of Lax pair and infinite number of conservation laws. The Darboux transformation is expressed in terms of Casorati type determinant. Further, by combining the Darboux transformation with different solutions of eigenfunction, we provide a comprehensive approach to construct various types of exact solutions to the spatially discrete Boussinesq equation, such as multi-soliton solutions, periodic solutions, rational solutions and more generally their interaction solutions. Lastly, we prove that the theory of spatially discrete Boussinesq equation including the Lax pair, the conservation laws, the Darboux transformation and the exact solutions converges to the corresponding theory of the Boussinesq equation in the continuum limit.
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