- Hacettepe Journal of Mathematics and Statistics
- Vol: 52 Issue: 1
- Differential geometric approach of Betchov-Da Rios soliton equation
Differential geometric approach of Betchov-Da Rios soliton equation
Authors : Yanlin Li, Melek Erdoğdu, Ayşe Yavuz
Pages : 114-125
Doi:10.15672/hujms.1052831
View : 13 | Download : 3
Publication Date : 2023-02-15
Article Type : Research
Abstract :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 $\\Phi=\\Phi(s,t)$ 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.Keywords : Betchov-Da Rios equation, localized induction equation (LIE), smoke ring equation, vortex filament equation, nonlinear Schrodinger (NLS) equation.