Integrable Kuralay Equations: Geometry, Solutions and Generalizations

Zhanna Sagidullayeva, Gulgassyl Nugmanova, Ratbay Myrzakulov, Nurzhan Serikbayev

2022

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DOI 10.3390/sym14071374
Data confidence 85 high
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Abstract

In this paper, we study the Kuralay equations, namely the Kuralay-I equation (K-IE) and the Kuralay-II equation (K-IIE). The integrable motion of space curves induced by these equations is investigated. The gauge equivalence between these two equations is established. With the help of the Hirota bilinear method, the simplest soliton solutions are also presented. The nonlocal and dispersionless versions of the Kuralay equations are considered. Some integrable generalizations and other related nonlinear differential equations are presented.