On the modified discrete KP equation with self-consistent sources

• Published in: Journal of nonlinear mathematical physics Vol. 24; no. 2; pp. 224 - 238
• Main Authors: Gegenhasi, Bai, Xiaorong
• Format: Journal Article
• Language: English
• Published: Dordrecht Taylor & Francis 01-01-2017; Springer Netherlands; Springer Nature B.V
• Subjects: Commutativity; Continuum limit; Differential equations; Discrete Gram-type determinant; Modified discrete KP equation; Research Article; Source generalization procedure; Transformations (mathematics); 37K40; Source generalization procedure; Modified discrete KP equation; Continuum limit; 37K10; Discrete Gram-type determinant
• ISSN: 1402-9251; 1776-0852; 1776-0852
• DOI: 10.1080/14029251.2017.1313476

The modified discrete KP equation is the Bäcklund transformation for the Hirota's discrete KP equation or the Hirota-Miwa equation. We construct the modified discrete KP equation with self-consistent sources via source generation procedure and clarify the algebraic structure of the resulting coupled modified discrete KP system by presenting its discrete Gram-type determinant solutions. It is also shown that the commutativity between the source generation procedure and Bäcklund transformation is valid for the discrete KP equation. Finally, we demonstrate that the modified discrete KP equation with self-consistent sources yields the modified differential-difference KP equation with self-consistent sources through a continuum limit. The continuum limit of an explicit solution to the modified discrete KP equation with self-consistent sources also gives the explicit solution for the modified differential-difference KP equation with self-consistent sources.