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.
