Soliton surfaces induced by the Fokas-Lenells equation

In this paper, we study the application of the theory of solitons in differential geometry. The recently proposed soliton equation, which is Fokas-Lenells equation, has been investigated, and its two-dimensional soliton surface in the three-dimensional Euclidean space (R² ! R³) has been constructed. Thus the connection between the Fokas-Lenells equation and the surface was established by using the Sym-Tafel formula. We find the first and the second quadratic forms, surface area, and Gaussian curvature. The obtained results have various applications in mathematical physics, the geometry of curves and the theory of surfaces.