Geometrical Features of the Soliton Solution

Abstract

It is well known, that integrable equations are solvable by the inverse scattering method (Ablowitz and Clarkson in Solitons, Non-linear Evolution Equations and Inverse Scattering, 1992). Investigating of the integrable spin equations in (1+1), (2+1) dimensions are topical both from the mathematical and physical points of view (Lakshmanan and Myrzakulov in J. Math. Phys. 39:3765–3771, 1998; Gardner et al. in Phys. Rev. Lett. 19(19):1095–1097, 1967). Integrable equations admit different kinds of physically interesting solutions as solitons, vortices, dromions etc. We consider an integrable spin M-I equation (Myrzakulov and Vijayalakshmi in Phys. Lett. A 233:391–396, 1997). There is a corresponding Lax representation. And the equation allows an infinite number of integrals of motion. We construct a surface corresponding to soliton solution of the equation. Further, we investigate some geometrical features of the surface.