Integrable Kuralay Equations: Geometry, Solutions and Generalizations
Zhanna Sagidullayeva, Gulgassyl Nugmanova, Ratbay Myrzakulov, Nurzhan Serikbayev
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.
Topics & Concepts
Integrable systemMathematicsEquivalence (formal languages)Independent equationBilinear interpolationNonlinear systemDispersionless equationMathematical analysisDifferential equationSolitonMotion (physics)Space (punctuation)Differential geometry of curvesMathematical physicsDifferential algebraic equationPhysicsPure mathematicsClassical mechanicsKadomtsev–Petviashvili equationOrdinary differential equationBurgers' equationQuantum mechanicsStatisticsLinguisticsPhilosophyNonlinear Waves and SolitonsAlgebraic structures and combinatorial modelsFractional Differential Equations Solutions