A Natural Full-Discretization of the Korteweg-de-Vries Equation

被引：0
作者：
Hu, Xingbiao [1 ,2 ]
Zhang, Yingnan [3 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[3] Nanjing Normal Univ, Sch Math Sci, Nanjing 210024, Jiangsu, Peoples R China
来源：
NONLINEAR AND MODERN MATHEMATICAL PHYSICS, NMMP 2022 | 2024年 / 459卷
基金：
中国国家自然科学基金;
关键词：
Integrable discretization; Korteweg-de-Vries equation; Backlund transformation; NONLINEAR EVOLUTION-EQUATIONS; BACKLUND-TRANSFORMATIONS; DIFFERENCE-EQUATIONS;
D O I：
10.1007/978-3-031-59539-4_6
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we propose an integrable full-discretization of the Kortewegde-Vries (KdV) equation. Our method is based on the compatibility between the integrable equation and its Backlund transformation. By using this approach, we derive a discrete equation that is a natural discretization of the KdV equation. Specifically, in the natural limit, the discrete system approaches the continuous KdV equation. We demonstrate that the integrability of the discrete system is confirmed by a Lax pair and a Backlund transformation.
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页码：175 / 187
页数：13
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