Symmetric discrete AKP and BKP equations. (28th January 2021)

• Record Type: Journal Article
• Authors: Li, Shangshuai; Nijhoff, Frank W; Sun, Ying-ying; Zhang, Da-jun
• Is Part Of: Journal of physics. Volume 54:Number 7(2021)
• Publication Date: 2021-01-28
• Subjects: discrete AKP -- discrete BKP -- symmetric tau function -- solution -- elliptic function; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/abd998
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We show that when KP (Kadomtsev–Petviashvili) τ functions allow special symmetries, the discrete BKP equation can be expressed as a linear combination of the discrete AKP equation and its reflected symmetric forms. Thus the discrete AKP and BKP equations can share the same τ functions with these symmetries. Such a connection is extended to 4 dimensional (i.e. higher order) discrete AKP and BKP equations in the corresponding discrete hierarchies. Various explicit forms of such τ functions, including Hirota's form, Gramian, Casoratian and polynomial, are given. Symmetric τ functions of Cauchy matrix form that are composed of Weierstrass σ functions are investigated. As a result we obtain a discrete BKP equation with elliptic coefficients.