Differential geometric approach of Betchov-Da Rios soliton equation

Authors : Yanlin Lİ, Melek ERDOĞDU, Ayşe YAVUZ

Pages : 114-125

Doi:10.15672/hujms.1052831

View : 20 | Download : 10

Publication Date : 2023-02-15

Article Type : Research Paper

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 $\\Phi=\\Phiinsert ignore into journalissuearticles values(s,t);$ 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