Differential geometric approach of Betchov-Da Rios soliton equation

Year 2023, , 114 - 125, 15.02.2023

Yanlin Li Melek Erdoğdu , Ayşe Yavuz

https://doi.org/10.15672/hujms.1052831

Cited By: 24

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

Supporting Institution

National Natural Science

Project Number

12101168

Thanks

This work was funded by the National Natural Science Foundation of China (Grant No. 12101168).

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