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.
Betchov-Da Rios equation localized induction equation (LIE) smoke ring equation vortex filament equation nonlinear Schrodinger (NLS) equation
National Natural Science
12101168
This work was funded by the National Natural Science Foundation of China (Grant No. 12101168).
Betchov-Da Rios equation localized induction equation (LIE) smoke ring equation vortex filament equation nonlinear Schrodinger (NLS) equation.
12101168
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Mathematics |
Authors | |
Project Number | 12101168 |
Publication Date | February 15, 2023 |
Published in Issue | Year 2023 Volume: 52 Issue: 1 |