Open AccessSoliton surfaces induced by the Fokas-Lenells equation
Author(s) -
Kuralay Yesmakhanova,
Meruyert Zhassybayeva,
Ratbay Myrzakulov
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1416/1/012042
Subject(s) - gaussian curvature , soliton , surface (topology) , connection (principal bundle) , curvature , differential geometry , euclidean space , mathematics , quadratic equation , mathematical analysis , euclidean geometry , partial differential equation , geometry , mathematical physics , physics , classical mechanics , quantum mechanics , nonlinear system
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 (R 2 ! R 3 ) 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.