Differential geometric approach of Betchov-Da Rios soliton equation

In the present paper, we investigate differential geometric properties the soliton surface M associated with Betchov-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 Betchov-Da Rios equation to be a minimal surface. Finally, we examine a soliton surface associated with Betchov-Da Rios equation as an application.