Integrable Kuralay Equations: Geometry, Solutions and Generalizations
Zhanna Sagidullayeva,
Gulgassyl Nugmanova,
Ratbay Myrzakulov,
Nurzhan Serikbayev
Affiliations
Zhanna Sagidullayeva
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, 010009 Nur-Sultan, Kazakhstan
Gulgassyl Nugmanova
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, 010009 Nur-Sultan, Kazakhstan
Ratbay Myrzakulov
Department of General and Theoretical Physics, Department of Mathematical and Computer Modeling, Eurasian National University, 010008 Nur-Sultan, Kazakhstan
Nurzhan Serikbayev
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, 010009 Nur-Sultan, Kazakhstan
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.
