Hasimoto surfaces for two classes of curve evolution in Minkowski 3-space

• Autorzy: Gürbüz Nevin , Yoon Dae Won

Identyfikatory

DOI

10.1515/dema-2020-0019

• Języki publikacji: EN

Abstrakty

EN

In this work, we study Hasimoto surfaces for the second and third classes of curve evolution corresponding to a Frenet frame in Minkowski 3-space. Later, we derive two formulas for the differentials of the second and third Hasimoto-like transformations associated with the repulsive-type nonlinear Schrödinger equation.

Słowa kluczowe

EN

Hasimoto surface; nonlinear Schrödinger equation; time evolution

PL

równania nieliniowe; równanie Schrodingera

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2020
• Tom: Vol. 53, nr 1
• Strony: 277--284
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Gürbüz Nevin

• Mathematics-Computer Department, Eskişehir Osmangazi University, Eskisehir, Turkey

autor

Yoon Dae Won

• Department of Mathematics Education and RINS, Gyeongsang National University,Jinju, 52828, Republic of Korea

Bibliografia

• [1] H. Hasimoto, Motion of a vortex filament and its relation to elastic, J. Phys. Soc. Jpn. 31(1971), 293-294, DOI: 10.1143/JPSJ.31.293.
• [2] M. Lakshmanan, Continuum spin system as an exactly solvable dynamical system, Phys. Lett. A. 61(1977), 53–54, DOI: 10.1016/0375-9601(77)90262-6.
• [3] Jr G. L. Lamb, Elements of Soliton Theory, John Wiley & Sons, New York, 1980.
• [4] T. Langer and P. Perline, The Hasimoto transformation and integrable flows on curves, Appl. Math. Lett. 3(1990), 61–64, DOI: 10.1016/0893-9659(90)90015-4.
• [5] S. Murugesh and R. Balakrishnan, New connections between moving curves and soliton equations, Phys. Lett. A. 290(2001), 81–87, DOI: 10.1016/S0375-9601(01)00632-6.
• [6] N. Gürbüz, The differential formula of Hasimoto transformation in Minkowski 3-space, Int. J. Math. Math. Sci. 16(2005), 2609–2616, DOI: 10.1155/IJMMS.2005.2609.
• [7] N. Gürbüz, Intrinsic geometry of NLS equation and heat system in 3-dimensional Minkowski space, Adv. Stud. Theor. 4(2010), 557–564.
• [8] N. Gürbüz, Three classes of non-lightlike curve evolution according to Darboux frame and geometric phase, Int. J. Geom. Methods Mod. Phys. 15(2018), 1850023, DOI: 10.1142/S0219887818500238.
• [9] N. Gürbüz, Anholonomy according to three formulations of non-null curve evolution, Int. J. Geom. Methods Mod. Phys. 14(2017), 1750175, DOI: 10.1142/S0219887817501754.
• [10] N. Gürbüz, Three anholonomy densities according to Bishop frame in Euclidean 3-space, J. Math. Phys. Anal. Geom. 15(2019), 510–525, DOI: 10.15407/mag15.04.510.
• [11] N. Gürbüz, Total anholonomies with Bishop 2-type frame in R13, Nonlinear Anal. Diff. Equ. 7(2019), 115–124, DOI: 10.12988/nade.2019.9914.
• [12] N. Gürbüz, Moving non-null curves according to Bishop frame in Minkowski 3-space, Int. J. Geom. Methods Mod. Phys. 12(2015), 1550052, DOI: 10.1142/S0219887815500528.
• [13] W. K. Schief and C. Rogers, Binormal motion of curves of constant curvature and torsion. Generation of soliton surfaces, Proc. R. Soc. Lond. A. 455(1999), 3163–3188, DOI: 10.1098/rspa.1999.0445.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).