Differential Geometric Approach of Betchow-Da Rios Soliton Equation

In the present paper, we investigate differential geometric properties the soliton surface M associated with the Betchow-Da Rios Equation. Then, we give derivative formulas of Frenet frame of unit speed curve Φ=Φ(s,t) for all t. Also, we discuss the linear map of Weingarten type in the tangent space of the surface that generates two invariants: k and h. Moreover, we obtain the necessary and sufficient conditions for the soliton surface associated with the Betchow-Da Rios Equation to be minimal surfaces. Finally, we examine an soliton surface associated with the Betchow-Da Rios Equation as an application.