Geometric flows along acceleration vector field of null curves
Zühal Küçükarslan Yüzbaszuhal2387@yahoo.com.trDepartment of Mathematics Fırat UniversityElazig, 23119, TurkeyView full profile → , Ebru Cavlak Aslanebrucavlak@hotmail.comDepartment of Mathematics Fırat UniversityElazig, 23119, TurkeyView full profile → , *Dae Won YoonCorresponding authordwyoon@gnu.ac.krDepartment of Mathematics Education and RINS Gyeongsang National UniversityJinju, 52828, Republic of KoreaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Dec 2023
- Published Online:
- 14 May 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2443
- Pages:
- 1–15
Abstract
Keywords
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References
[1] N.H. Abdel-All and M.T. Al-Dossary, “Motion of curves specified by acceleration field in Rn,” Applied Mathematical Sciences, vol. 7, no. 69, pp. 3403-3418 (2013).
[2] S.C. Anco and E. Asadi, “Hasimoto variables, generalized vortex filament equations, Heisenberg models and Schrödinger maps arising from group-invariant NLS systems,” Journal of Geometry and Physics, vol. 144, pp. 324-357 (2019).
[3] M.E. Aydin, A. Mihai, A.O. Ogrenmis and M. Ergut, “Geometry of the solutions of localized induction equation in the pseudo-Galilean space,” Advances in Mathematical Physics, Article ID 905978, p. 7 (2015).
[4] Q. Ding and J. Inoguchi, “Schrodinger flows, binormal motion for curves and the second AKNS-hierarchies,” Chaos Solitons Fractals, vol. 21, no. 3, pp. 669--677 (2004).
[5] Q. Gamayun and Q. Lisovyy, “On self-similar solutions of the vortex filament equation,” Journal of Mathematical Physics, vol. 60, no. 4, 083510 (2019).
[6] M. Grbovic’ and E. Nešovic’, “On Bäcklund transformation and vortex filament equation for null Cartan curve in Minkowski 3-space,” Mathematical Physics, Analysis and Geometry, vol. 19, Article number: 23 (2016).
[7] N. E. Gürbüz and D. W. Yoon, “Visco-Da Rios equation in 3-dimensional Riemannian manifold,” Frontiers in Physics, vol. 9, Article 810920 (2022).
[8] N.E. Gürbüz, Z.K. Yuzbasi and D.W. Yoon, “Hasimoto Maps for Nonlinear Schrödinger Equations in Minkowski Space,” Journal of Nonlinear Mathematical Physics, vol. 29, pp. 761-775 (2022).
[9] M. Inc, E. Ulutas, E.C. Aslan and A. Biswas, “Singular 1-Soliton Solution of the K(m, n) Equation with Generalized Evolutions and its Subsidiaries,” Acta Physica Polonica B, vol. 44, no. 9, pp. 1825-1836 (2013).
[10] M. Kass, A. Witkin and D. Terzopoulos, “Snakes: active contour models,” in: Proc. 1st Int. Conference on Computer Vision, pp. 259-268 (1987).
[11] T. Körpinar and E. Turhan, “Inextensible flows of biharmonic S-curves according to Sabban frame in Heisenberg group Heis3,” Journal of Interdisciplinary Mathematics, vol. 21, no. 1, pp. 17-27 (2018).
[12] G. Muiraja and G. Lakshmanan, “Motion of space curves in 3-dimensional Minkowski space R13, SO(2,1) spin equation and defocusing nonlinear Schrödinger equation,” International Journal of Geometric Methods in Modern Physics, vol. 7, no. 6, pp. 1043-1049 (2010).
[13] T. Tsurumi, H. Segur, K. Nakayama and M. Wadati, “Motion of curves specified by accelerations,” Physics Letters A, vol. 224, no.4-5, pp. 253-263 (1997).
[14] A. Yavuz and M. Erdoğdu, “Congruence of generate surface along pseudo null curve and Landau-Lifshitz equation,” Journal of Geometry and Physics, vol. 178, p. 104553 (2022).
[15] D.W. Yoon, Z.K. Yüzbas and E.C. Aslan, “Evolution of space-likes and special time-like ruled surfaces in the Minkowski space,” Indian Journal of Physics, vol. 96, pp. 995-999 (2022).
[16] Z.K. Yüzbas and S.C. Anco, “Elastic null curve flows, nonlinear C-integrable systems, and geometric realization of Cole-Hopf transformations,” Journal of Nonlinear Mathematical Physics, vol. 27, pp. 357-392 (2020).
[17] Z.K. Yüzbas, “A new approach to the connections between moving curves and a family of complex KdV type systems,” Mathematical Methods in the Applied Sciences, vol. 46, no. 4, pp. 4279-4288 (2023).
