A Study on the Semi-Discrete KP Equation: Bilinear Bäcklund Transformation, Lax Pair and Periodic Wave Solutions

Chunxia Li, Linshuo Wan and Hongyan Wang ()
Additional contact information
Chunxia Li: School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
Linshuo Wan: School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
Hongyan Wang: School of Mathematics, Renmin University of China, Beijing 100872, China

Mathematics, 2025, vol. 13, issue 21, 1-13

Abstract: In this paper, we investigate the integrability and solution structure of the semi-discrete KP equation. A bilinear Bäcklund transformation, Lax pair, and nonlinear superposition formula are systematically derived, establishing the integrability of the system. Furthermore, one- and two-periodic wave solutions are constructed using Hirota’s method combined with Riemann theta functions. By means of a rigorous limiting procedure, the asymptotic behavior of the periodic wave solutions is analyzed, and the connection between periodic wave and soliton solutions is established. These results not only enrich the solution structure of the semi-discrete KP equation but also provide new perspectives on periodic phenomena in discrete integrable systems.

Keywords: Bäcklund transformation; nonlinear superposition formula; Riemann theta function; periodic solution; soliton solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/21/3492/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/21/3492/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:21:p:3492-:d:1785154

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().